In fact, I am not going to follow the sequence of the slides that he has given, but I was looking at the interaction that you had. I will try to indicate to what should I say practical examples of one example of what we call denormalization, which is often required. The other is the issues about including temporal aspects in your database design. There are slides, I do not know in the abbreviated version the slides are there or not. Let me very quickly mention the more important practical aspect, which is the third normal form. As a matter of fact, you will recall, because this is what I have seen in most courses on databases. We actually teach first normal form, second normal form, third normal form and BCNF is often thought as a subsequent thing to turn normal. That is often the sequence of teaching. Technically what Sudarshan has emphasized is right. BCNF is the core normal form and a diluted version is actually third normal form. So, I do not know whether that gets emphasized in our teaching or not. Ideally, we should get BCNF, we cannot get BCNF, we get CNF. Some of these slides indicate what are the situations under which we might be required to do this. Why is third normal form important? I will skip these slides, because they say essentially that third normal form is a weaker form of BCNF. To the extent it is weaker, that could be indicated how it is weaker. Basically, if BCNF is not dependency preserving and if efficiency is a problem, then you could incorporate it. So, for example, you want to guarantee that there is always a lossless joint. A lossless joint can be guaranteed if you have this thing is in the third normal. You might permit some redundancies in the process. So, here is an example of the third normal form. But rather than going through these slides, as I said, some of these would be covered during the tutorial problems, I will indicate one observation, which I think Prasudarshan has also made. Canonical cover is an important theoretical concept. Again, there are algorithms which will determine that canonical cover and you can actually go through that. You can compute the canonical cover and then devise the CNF decomposition algorithm from canonical cover. What I am going to very briefly describe is the practical way of doing things. The practical way of doing things is actually to start with a good model. So, you take a rudimentary model, an ER model. If your ER model is well designed, then invariably the schema that you will get by translating those relationships and associations will be in CNF and that is what is often done in practice. I have seen hundreds upon hundreds of cases of real-life database design. Hardly 5 to 10 percent of those cases, the designers have bothered to actually apply functional dependency algorithms and cross check very rigorously for what that is. Hardly 5 to 10 percent. That is the unfortunate consequence of theory not being practiced rigorously. However, most designs in real life do derive from a good model. So, the emphasis is on modeling. If you have taken care of identifying all entities properly and particularly identifying what looks like an attribute of an entity but should be an independent entity. A clear example in the case of the schema that we are discussing is department. You might inadvertently consider department to be an attribute of a teacher, for example, because the teacher belongs to a department. But if you look at the fact that department has a building, department has a budget, etcetera, etcetera, at the modeling stage itself, you would recognize that department is a separate entity. Now, if you do that, you will have a model in which you will say, so this is let us say my teacher and I have the ID and I have everything else and let us say somewhere here when I say department, I recognize that department is an entity. So, I remove it and I make department as a separate entity. If I make department as a separate entity, then I have a department ID, I have a department building, I have a department budget, etcetera, etcetera, and then I can set up a relationship. You will notice that what we were trying to do earlier through a mechanism of decomposition. So, decomposition theoretically assumes that all the attributes of the schema you have assembled into a single relation first and then you are trying to decompose it into multiple relation. In real life, that does not happen. In real life, you will start with relations which replant different entities and which replant different association sets. And when you model them into your schema, you will find invariably, you will get a decent schema. Take for example, a student and a course relation. When you model course independently, when you model student independently and when you do not involve a teacher anywhere here, then the basic entity of course is modeled. There is no issue of update anomaly as you mentioned. You can update any field which because every non key attribute is fully and non functionally dependent upon the key attribute that you have identified, which is the crux of the third normal form as we say non transitive dependence. So, if we have that, you will find that the table that you get, say text or register for whatever you name, you will have essentially the primary key from here. So, this is let us say role and primary key from here, let us say course ID. Now, when you get this, this relation is third normal form, this relation is in third normal form, this relation is third normal form. This is the way practically people determine their scheme. Very rarely people test these things. Now, what is our emphasis? Why we want to do this? There are two aspects according to me. This entire chapter of decomposition is important from a theoretical perspective, fundament. People must understand why we are doing all this and if we do not do it, what does it imply? What does it imply if I cannot preserve a dependency? There could be significant consequences in the actual operations. When I update things, when I insert things, when I do changes in my database, would they preserve the properties that originally were conceived to be valid for that entire data? It is from that point of view, you must do this. Secondly, you would expect that at least some of your students who join organizations such as Infosys, TCS, etc., etc., etc., and when they do database design, they are aware that in addition to the mundane mapping of your ER model into schema, something extra should be done, something extra should be tested. You will invariably find such testing being done in the top-notch organizations when they do schema. So, TCS will do that, Infosys will do that, Wipro will do that, HCL will do that, but there are hundreds upon hundreds of organizations and many of our students are currently doing good jobs in these organizations. Should we not expect them, A, to be fundamentally aware of what these things are? B, to be aware of what are the algorithms in case they wish to apply them? And C, with that knowledge, perhaps some people will proactively do it. Some others will do it because the organization demands it. That is the real-life story. It is in this context that rather than the closure of the functional dependencies, the attribute closure appears to me to be an important point because you can apply that logic practically, examining things on smaller relations much more easily rather than finding out the cover. There are tools by the way, database design tools where you can input functional dependencies and you can determine the canonical cover, etcetera. So, when you have 10 or 20 attributes, that is trivial, but when you have 200 attributes, it is very difficult. In general, in real life, in large applications, you will always begin with a set of different relations. You will never have a single relation containing all 10,000 attributes that the corporate world defines. So, you will have several independent relations. It is possible to apply these algorithms on these independent relations. And my suggestion is emphasize to the students, indicate to them the algorithm for the functional dependency closure as well as the attribute closure and suggest that looking at the attribute closure, they can practically apply it very quickly to determine whether something is preserved or not. So, I will just say this. These things would be covered in a tutorial, I think, some problem. You have a 3NF decomposition problem? Is it that? In the tutorial? Yeah, okay. So, we will just take it up. I needed to do something else. So, this is an important side. The goal for a relational database design is ideally BCNF, lossless joint and dependency preservation. But if we cannot achieve all of this, then we may either have lack of dependency preservation or you may have redundancy due to the use of 3NF. And the real world goes after this option approach. I will use 3NF. I still preserve dependencies, but I do not mind some redundancy if I get, okay. Now, this is the dilemma that SQL per se does not have any constructs, which will guarantee any one of these things. SQL faithfully implements whatever you tell it to improve. So, the constraints that you define will be implemented. And that's another reason why I, when I intervened, I said that one should be very careful in defining constraints at the SQL data definition level. This is in contrast to what I said on the first day. We must implement all constraints as database definition constraints and not implement them through PLA SQL or something else. Because that's a feature that SQL provides now. However, what constraints you determine to be defined at the database level should be carefully done. So, all constraints which are not only valid today for the organization, but which are likely to remain valid for a long time to come should definitely be implemented as database constraint definitions. All other constraints, there should be a considered view. What should we take? In fact, in many of the course projects, which are team projects, we ask them to do a fancy stuff. Whenever they take a design decision in a final report, only the decision will appear that this is my schema, etc. What we ask them is what alternatives did you consider? And what is the reason for rejecting those alternatives? That is where the application of mind happens. It is not that you will in one shot get just the final result which is submitted. That thinking process, we should advise our students and collect teachers. In fact, in December, that thinking process should be captured. So, what are the alternatives they consider? For example, for even the schema, what are the functional dependencies they actually wrote now? Did they examine whether this functional dependency is preserved or not? Many times, you will find that in the, particularly for the students who are in a hurry to submit something, they will either not apply their mind on these alternatives or even if they do, they will not incorporate it in the report. I think it is important for us to emphasize they do both because that is where thinking happens. And if you permit them to force them to think and ask them to capture that thinking in a report, it will help. Now, what I propose is that even though the teacher's workshop is only a 10-day duration. We call it technically two weeks because ISTA recognition of two-week workshop is useful for the teachers. However, in 10 days, it may or may not be possible for them to do all of this. So, that is why we will form teams right from the first day. And this time, we will advise teachers that they will have to do a sort of project, part of which they have to do it within the workshop and part of which they have to do it later. And I would like you to emphasize this when you deal with teams of the teachers who come to your place because if teachers understand the importance of thinking of alternatives, writing those down, reporting them, then it is likely that they will insist that the same thing be done by students later. I think that is what is important. So, very quickly, let me just mention. I am going to skip multi-valued dependencies. So, when an ER model is carefully designed, identifying entities correctly, the tables generated from ER diagram should not need further normalization. However, when you translate an ER model into a schema, you will not necessarily get BCNF. But invariably, almost without exception, you will get it into a third normal form if your basic identification of entities is correct. And the key point in the design process to tell people is to say that, please look at each attribute of an entity that you have identified and imagine whether that attribute itself could be a separate entity. That is where given a set of attributes, when you later on say that this depends only on this subset and that depends only on that subset, what are we saying? Effectively, we are saying that by mistake, two different entities have got mixed up in one table. So, looking at it while modeling is a much easier and a much better process. Now, that emphasis again is not indicated. Perhaps these examples in the decomposition could be used to construct examples of a good ER model itself. While modeling, how for example, a department may be mistakenly written here and then it needs to be identified as a separate entity could be emphasized, that will result in a better process. There is one more thing here. Temporal data is extremely hard to handle. So, this is one example I wanted to give you how to handle temporal data. Temporal data means time. Time actually with time things change, but we are unable to record what was the information in this time or that time because usually when you update a table, the current information is present. Take a simple case. Take for example, all of us faculty position. Let us say HR database is there and my situation, my current position, my current salary is maintained in a table. I update it, my current salary is so and so. What about the past record? When the government of India says such and such pay commission will apply from this date, that date is usually 5, 6 years ago. Now, if my database has no information about what was my salary 6 years ago, there is no way you can apply thing. So, usually what happens even if you have a good database, people will go to their files, paper files and say, oh, this was a salary. This happens because we are unable to maintain data in a temporal fashion. So, there are temporal databases which we are not discussing, but it is important to tell our teachers and through them to our students that temporal information is extremely important. I will give you a practical example of a situation where temporal information is required. Let us take insurance policies. Let us talk of general insurance. Let us say, a factory has been insured against fire or a car has been insured against this theft, that whatever. So, for everything insured, there is a peril. That means, it could be fire, accident, whatever, whatever. There is actually a sum insured, that is, insurance amount which is the premium that you pay, sorry, which is the sum insured which you will get in case of peril occurs and there is a premium amount that you pay. Let us say, this insurance policy number, say, P n is valid from, let us say, date 1 to date 2, which is typically 1 year. Three months later, a fellow comes and says, look, I had insured my car only against third party, but now I want comprehensive insurance even if there is accident I want to do. I have already paid this much premium. Whatever is the difference, premium I will pay now and please improve my policy to something or let us say, a factory was insured against fire. He wants to insure it against flood, which is another clause at a certain point in time. Now, a very curious situation happens. There is a D 1 dash here to D 2. He wants this policy P n to be modified to P n dash. If I had only a single database, I would update the policy terms, I will calculate the new premium, collect the difference and I will say this policy is valid up to D 2 with new terms. Exactly three days later, a claim comes from that fellow saying that such and such accident happened between D 1 and D 1 dash and what happened was my factory was flooded, please pay me. If I do not have this information about D 1 dash, then I will never be able to know that look that fellow is cheating. The flooding occurred actually here, but he was not covered for flooding at that point in time. This is a temporal incident. Consequently, what insurance companies all over the world including India do is they maintain versions and each version is effectively a separate P n dash, P n dash dash, P n dash dash, etcetera, etcetera and this is maintained through what is known as endorsements. So there is a policy there are certain terms. At certain date you say I want this additional cover, then an endorsement will be written. This endorsement effectively creates an equivalent of a new policy which is effective from D 1 dash to D 2 only. Another endorsement may come after two months. That endorsement may include the previous one or may nullify some of it. That will have to be maintained. Now if a claim comes against insurance saying that now give me this money, you examine the date of the event and you determine which of these versions apply to that date. Then you look at only those conditions which are printed or which are stored at that point in that version and then examine whether the claim is justified against those rules. If there are certain endorsement in a policy's life, there will be ten versions that will have to be maintained. All of them will have to be maintained either as current database because any time a claim comes you want to sort of locate that date. This is one way of maintaining temporal information. Invariably in many practical situations such as teacher's salaries or any HR system, etcetera, etcetera, you have what is known as a current info table and you have a history table. For practically each schema relation where changes need to be preserved in time. So, typically you take an employee's information wherever you have that will have to be preserved in time. Even a course, take a course. The course credits were six credits. CPI was calculated as per six credits or in most university norms. Let's say it was a 100 mark paper. The university changes that norm and says this paper will now be 75 marks. The name of the subject is same. The syllabus is same. Everything is same. Marks is 75. That is fine. The students who take that exam from this year onwards they will be evaluated for 70. Generally one gentleman from Jharsukura comes and says three years ago I had failed. Now I am appearing for this course. Now that fellow has to be given marks out of 100. This is a non-trivial business requirement. How do you handle that? So, you preserve such information into history table. It is not uncommon in many situations to find that if you are let's say 100 table schema, then at least for 30 tables you will have additional 30 history tables. So, for example, an employee salary changes. The change in salary will be implemented in the current table. But you will insert a history record there which will say old salary this much. That means from this date to whenever something changes from entry will be made in the history table. Two entry will be nothing. Whenever that salary changes again the next date there will be a two entry here and a new entry for the new salary new position whatever. Now it is a question how many fields you provide for changes. So, you do not. You just provide information and you just have a from and to date saying this row is valid from this date to this date. Even if let's say designation changes some other time salary does not change. You will have same row where the designation will change but it will have a from and to date. Now obviously for an employee if let us say five of these attributes typically salary will change annually designation will change 3, 4, 5 times. There could be some other rules which will change. Every time a change occur one tuple goes in. And what should be the key for this tuple? Obviously the MPID will be there. But MPID is not adequate because the same MPID will have multiple rows here. So, people artificially put a serial number or sequence number. So, MPID plus serial number MPID plus serial number. If there are 20 rows MPID plus these 20 one MPID 2 MPID 3 MPID 20 and the employee's current record. It is not difficult to write SQL queries for this. You give us employee code from one SQL query you extract information about that employee from the current table by another SQL query. You extract all the 20 rows or 50 rows of activity and all these rows together represents the information about that employee. So, this is a minimal way in which the temporal information has to be taken care of in real life. Unfortunately the conventional database theory that has emerged because in the beginning it emphasized preserving current information. So, that is what update is. You know update means remove present information and put something else. It does not take care of the temporal preservation of that information. This has to be done. Let me very quickly describe the denormalization requirement by giving you an example which we just encountered in a large data warehouse designed for SEBI. SEBI is the securities and exchange board of India and it supervises operations in stock trading across the country. There are two major stock trading agencies. One is Bombay Stock Exchange, one is National Stock Exchange, BST and NSC. How you buy and sell securities? All of you are familiar with stocks, but most people like us do not do speculation, do not do day trading. We buy a stock sometimes, we sell a stock sometimes, price goes up, etcetera. In real life that is not what happens. People will buy, keep buying and then they will keep selling. At the end of the day they might have zero money exchange. They might have zero stocks exchange, but they would have done maybe 100 crore worth of buying and selling in the process. The procedure of day trading or any trading for that matter because you cannot distinguish between day trading and the regular trading from the nature of the input that you get in the stock exchange. So, you will get for example, what is known as orders. So, order data will mention let us say L and T script and I want to buy or to sell. So, there will be my name for example, ID, my ID. I am placing an order for buying or selling these things. I will mention a quantity and I will mention a price. When I make this offer, if there is a if there is an offer that I am making for buying, if somebody is giving an offer for selling and if things match, it will result in an actual transaction. But if it does not, this order will remain. After sometime I can put a fresh order. I can put another order. I can put quantity 10, 20, 30, etc. at different prices.  It is not uncommon to have something like 10 million such orders. What happens is some of them result in an actual transaction. And that is called a buy and sell record. So, that buy and sell record is buy. So, who bought it? Who? Quantity, price and sell. Again who? So, who sold? Who bought? The quantity and price must be agreed upon prices. This is one record that gets inserted. Obviously, there is a separate table for preserving this. There is a separate table for maintaining all this. What is the SEBI's problem? SEBI is typically interested in investigating whether people are doing some artificial transactions and causing the price to increase in the market. Because all this information is available to everyone. And if there is a lot of people buying, buying, buying, people will say, oh my God, the price will go up. Let me also buy. And that way the price actually goes up. And the original fellows who designed this artificial stuff walk out after selling of whatever they have got at higher price. They make a killing. And the other fellows are left in the large. So, there are about 20 different ways of doing some fancy stuff which are well known and identified in the stock market itself. One is called circular trading. So, I sell to you, you sell to me. I sell to you, you sell to me. What is happening? I am increasing the volume of things being sold. So, suddenly people believe there is a lot of activity, important share and the market price will go up. I am buying and selling at roughly the same price. So, we are not affected. We are friends. But somewhere in the afternoon we both will decide. So, we will make money and get out. But this is considered bad way. Now, the SEBI will like to catch us. How will it catch us? Because we are placing orders. The actual execution may or may not happen. Or when it happens, if it happens between me and him consistently, I need to catch. How will I do that? I will do that by taking a join of this and this. There are additional squiggles. I want the cumulative quantity that has been ordered by someone for buying or that has been ordered by someone for selling at the time when the sale or buy occurred. There is a time id which is most important. There is a time id here also. So, how do I calculate the cumulative sale, a cumulative quantity of orders that I have placed? Up to the point where the actual transfer occurred, I will have to add up this quantity, this quantity, this quantity from one particular individual. There will be millions of them, from one particular individual. Up to the time that that individual name appears in actual buying or selling. So, that is the cumulative quantity. Essentially, we are saying that we will require to join these two. Without joining, we cannot have that. Well, easy. Join is a standard thing that we do. The only problem is, I may have, let us say, 100 million rows here and about 10 million rows here. How will you find out? Now, this is for one day. The circular trading has to be observed over a period of time. And that period of time has to be a moving window for six months. How do you do that? You see the tough real-life problem. Efficiency is of a fundamental concern because I want to catch these culprits as early as possible, preferably in real time, preferably by tomorrow morning. It won't help if my join takes about 36 hours to execute. And we are not talking of small PCs and the netbooks. We are talking of very large machines. And still, the data is very large. So, the typical data warehouse data which will sit for one year is of the order of four terabytes. And they will, they have to preserve data for about seven sort of years or something because investigations, when they start, what happened then? There was a problem here. That is how scams get caught. They have one of the most wonderful surveillance systems in the world today. I know because I was fortunate to lead that effort from the technical side. But here is a question. When you do a benchmark, if these queries have to be run very frequently by different investigating teams, then you can't obviously say the whole machine can be used by just one person doing this query because simultaneously something else is happening. How do you handle this? So, the correct way is to recognize that, look, I can't spend time in joining these fields. They are proper third normal form. In fact, BCNF schemas individually if you look at it. There is no dependency. They are independent activity. The way you denormalize is that you recognize that every time an actual buy or sell occurs, you can construct two artificial order records. One called order for buy. Another for order for sell. But you flag it by saying that this is the actual culmination into an activity. So, what you do is you take this and break it into two record, a buy order and a sell order. And you put both of these back into this scheme. So, you have already 100 million such orders because orders you keep placing. Only when sometimes the matching will occur, you will say, okay, I buy at this rate or something. There will be multiple such orders. Now, whenever this order has happened, the same time, the same time id, but who placed an order for buy means he actually bought, but who placed an order for buy, what quantity I will insert it there with that time. And I will put an additional flag, say actual transaction Z t. All of these will have false, false, false, false, false. There will be two records which will say true, true, false, false, false, false. Now, if I simply access this table in the time order sequence, in the time id sequence, and then I make a query that what was the cumulative amount which was ordered by db for buy up to the point when he actually bought. I don't have to do any join. My query is on a single tape. In fact, a large number of such queries of this time of detecting fraudulent behavior can be done on a single tape. But what about update? Fortunately, in a data warehouse, you don't update because things which have happened in real life are being recorded. In real life, you may have to provide for update. Consequently, what you do is you have this table, you have this table and you may create a view. And while uploading the data into the database, you materialize that view. So, effectively, you have a third table which is as big, but it preserves this. Alternately, you will say why do this Godagiri? Because all other information that I want from this order table is available. If I say I will look at that table for other pieces of information by neglecting such records which have this here, then I have only the pure order information. So, I am augmenting this order table by something which really is not a dummy order, which is actually a transaction. Now, this example I thought of giving because enormously increases the efficiency. So, just to give you a benchmark result, when we are doing this benchmark test for what we call the worst rates and such other things, typical execution time when we are attempting to do joins was of the order of 36 minutes. And when we change this, that change of course requires for all seven years you will have to put the data like that. So, loading the data for seven years may take two days. But on a daily basis, it is not very difficult. On a daily basis, you take this table and push these data here. So, that is preprocessing that you have done. But after having done that, the order was about 4.5 seconds. I hope you appreciate the difference between a 4.5 second efficiency versus 36 minute efficiency. That is what you can get by normalization. This is probably an extreme example. Let me see if I can sort of get Savi's permission to pin this down and give this example as one of the additional examples which we could give to our teachers that this denormalization could be so useful. Now, it is a drastic example. But in normal case also, you do not run our normal applications on very large machines. So, there are realistic constraints even in real. So, consider a situation where a certain transaction, certain query will take 30 minutes or the order of several minutes versus of the order of several seconds. And if that query has to be done very frequently, then it is better to denormalize. This is one example of denormalization. I think I will stop here. Excuse me, professor. I have a question to ask regarding this Savi this thing. This is very big data. And as you said, in the past what has happened, these are just the facts and only kind of operation that is possible is the read operation mostly. So, are they trying to look at using some other data model which will facilitate the read type? The data model is being developed. But this is what the data model that has been finally, the physical data model and the logical data model are two different things. Logical data model has usually what you see in the data warehouse. But the physical data model is implemented with such denormalization in order to help the thing. This is not in tune with the kind of data modeling that we are discussing here because by and large the data warehouse data modeling is a different thing altogether. But I thought this to be a very good example of how much efficiency can be gained by denormalization. So, yes, you are right. It is only for read-only queries and there is no update which is possible. Because I think Google and other people are using kind of unstructured way of storing. In fact, at one point people thought that the database research has culminated into saturation and now people find that data management is throwing newer problems. So, this is a field which is alive. There is a conference called very large database conference which you remember I mentioned we conducted it in 1996 here. Now, what is very large has been changing. The first physical disk, if you remember the IBM introduced, it has a fantastic capacity of 7.25 megabytes. Big huge disk, this pack in fact 10 platters 7.25 megabytes. Why your thumb drives today have 4 GB, 8 GB, 16 GB easy. So, very large was once megabyte. Then sometimes it becomes gigabyte. Then it became terabyte. Today it is petabyte. The processing power has also increased and yet the problems at the critical age of functionality always demand more. And as an added attraction when the back end databases are increasingly being used by the web front ends and therefore the users who used to be 10 users, 20 users, 100 users, 10,000 users are now 1 color users. So, life is fun. I think we will conclude with that.


Hi and welcome to the session, I am Asha and I am going to help you solve following question which says verify whether the following are zeros of the polynomials indicated I mean spin. So first let us learn what is zero of the polynomial. Suppose we have a polynomial px then x is equal to c is called the zero of px if c is equal to zero. So this is the key idea we are going to use in this problem to find its solution. So all that you have to do to verify whether the certain given value of the variable is a zero of the polynomial or not just replace the variable in the given polynomial by the given value of the variable. Then if say value c gives pc is equal to zero where px is any polynomial then c is called the zero of the polynomial. Now let us see the first one which is px is equal to 3x plus 1 and we have to check that if x is equal to minus 1 upon 3 is a zero of the polynomial px or not. So on replacing x by minus 1 upon 3 in the polynomial px we have 3 into minus 1 upon 3 plus 1 and 3 cancels with 3 we have minus 1 plus 1 which is equal to zero. Thus we have p at minus 1 upon 3 is equal to zero. So we say that x is equal to minus 1 upon 3 is a zero of the given polynomial which is px is equal to 3x plus 1. So this completes the first part. Now proceeding on to the next one which is px is equal to 5x minus pi where x is equal to 4 upon 5. Now to check whether x is equal to 4 upon 5 is a zero of px or not let us substitute x by 4 by 5 and 5x minus 3. Now x is 4 upon 5 minus pi which is equal to 22 upon 7. 5 cancels out with 5 and we have 4 minus 22 upon 7. Now 4 can be written as 4 upon 1 and upon taking LCM of 7 and 1 we have 7 and in the numerator on dividing 7 by 1 we get 7. So multiplying the numerator 4 with 7 we have 28 minus 22 which is equal to 6 upon 7. Thus p at 4 upon 5 is equal to 6 upon 7 which is not equal to zero. Hence it is not a zero of the given polynomial px. As an answer is no, x is equal to 4 upon 5 is not a zero of the polynomial px which is equal to 5x minus pi. So this completes the second part. And now proceeding on to the third one where px is equal to x square minus 1 and we have to check whether x is equal to 1 and x is equal to minus 1 are the zeros of px or not. So first let us substitute x is 1 then we have 1 square minus 1 which is equal to 1 minus 1 which is further equal to 0. Thus we have p at 1 is equal to 0 and now let us find p at minus 1. So we have minus 1 whole square minus 1 which is equal to 1 minus 1 which is again 0 and hence again we have p at minus 1 is equal to 0. Thus the value of the polynomial px at x is equal to 1 and x is equal to minus 1 are both 0. Thus we can say that yes x is equal to 1 and x is equal to minus 1 are both the zeros px which is equal to x square minus 1. So this completes the third part and now proceeding on to the next one where px is equal to x plus 1 into x minus 2 and the values of x where we have to verify whether it is a 0 of px or not are minus 1 and 2. So first let us substitute x is equal to minus 1 in the given polynomial then we have minus 1 into minus 1 minus 2 which is further equal to 0 into minus 3 and on multiplying 0 with any number the result is 0. So we have p at minus 1 is equal to 0. Now let us find the value of the polynomial px at x is equal to 2. So replacing x by 2 we have 2 plus 1 into 2 minus 2 which is equal to 2 plus 1 is 3 and 2 minus 2 is 0 and again on multiplying 0 with any number the result is 0. So we have p at 2 is equal to 0 and thus we can say that x is equal to minus 1 and x is equal to 2 are the zeros of the given polynomial which is px is equal to x plus 1 into x minus 2. So this completes the fourth part and now proceeding on to the fifth one which is px is equal to x square and x is equal to 0. So to check whether x is equal to 0 is a 0 of px or not let us replace the variable x by 0 and let us give 0 square 0 square is equal to 0. So we have p0 is equal to 0 and thus we have a key idea. We can say that here is x is equal to 0 is the 0 of the given polynomial which is px is equal to x square. So this completes the fifth part and now proceeding on to the sixth part which is px is equal to lx plus m where x is equal to minus m upon l. So to check whether x is equal to minus m upon l as a solution of px or not let us replace the variable x by minus m upon l and we have l on the right inside and minus m upon l plus m and now l is common in the numerator and denominator on cancelling we are left with minus m plus m which is equal to 0. So we have p at minus m plus l is equal to 0 thus we can say that yes x is equal to minus m upon l is a 0 of the given polynomial which is px is equal to lx plus m and now proceeding on to the seventh one which is px is equal to 3x square minus 1 and the values of x are x is equal to minus 1 upon root 3 2 upon root 3. So first let us check whether x is equal to minus 1 upon 3 is a 0 of px or not. So replacing x by minus 1 upon root 3 in the polynomial we have 3 into minus 1 upon root 3 whole square minus 1 which is further equal to 3 and minus 1 upon root 3 whole square is 1 upon 3 minus 1 3 cancels out with 3 we have 1 minus 1 which is equal to 0 thus we have p at minus 1 upon root 3 is equal to 0 and now let us find whether x is equal to 2 upon root 3 is a 0 of px or not. So again replacing x by 2 upon root 3 in the polynomial we have 3 into 2 upon root 3 whole square minus 1 which is equal to 3 2 whole square is 4 and root 3 whole square is 3 minus 1 now 3 cancels out with 3 and we are left with 4 minus 1 which is equal to 3 hence p at 2 upon root 3 is equal to 3 which is not equal to 0 hence we can say that x is equal to minus 1 upon root 3 is a 0 px which is equal to 3x square minus 1 and x is equal to 2 upon root over 3 is not a 0 of the same polynomial which is 3x square minus 1. So this completes the part and lastly let us check whether x is equal to half is a 0 of px or not. So on replacing x by half in the polynomial px let us check what the value of the polynomial comes. So we have 2 into minus half plus 1 and 2 cancels out with 2 we have 1 plus 1 which is equal to 2 hence p at half is equal to 2 which is not equal to 0 therefore we can say that no x is equal to half is not a 0 of the given polynomial which is 2x plus 1. So this completes the last part and thus let us write the answers of each of the problems answer of the first part is yes the given value of x is a 0 of the polynomial. Second one is no answer to the third part is yes answer to the fourth part is yes answer to the fifth part is also yes answer to the sixth part is also yes and answer to the seventh part is that x is equal to minus 1 upon root 3 is a 0 but 2 upon root 3 is not a 0 and the last one is so this completes the solution so did you find this problem interesting it was easy now all you have to do is to replace the variable by the given value in the polynomial if the value of the polynomial comes 0 and this implies the given value of the variable is the 0 if it does not come to 0 then it is not a 0. So hope you enjoyed this session take care and have a good day.


Now, Roma Wines, R-O-M-A, made in California for enjoyment throughout the world. Roma Wines, present. Suspense.  A suspense play produced, edited and directed for Roma Wines by William Spear. Suspense, Radio's Outstanding Theatre of Thrills. It is presented for your enjoyment by Roma Wines. That's R-O-M-A, Roma Wines. Those excellent California wines that can add so much pleasantness to the way you live. To your happiness and entertaining guests. To your enjoyment of everyday meals. Yes, right now a glass bowl would be very pleasant. As Roma Wines bring you Mr. Joseph Cotton, in a remarkable tale of... Suspense. Save it, Walder. I've taken all of that I can.  Through. Sorry, sir. I couldn't help but overhear. What's the difference now? I hope you haven't quarreled seriously with your brother, sir. Quarold. What else have I ever done with him but quarreled? Well, I realize it's a bit difficult at times, but I'm sure he has your best interest at heart. Yeah, well, from now on he can stop worrying about my best interest, because I'm getting out of his life tonight, for good. I grabbed my hat and coat and rushed out of the house, looking wild-eyed and distracted.  Told him to go to the 23rd Street ferry. On the ferry, I stood by the stern rail. I walked up and down, puffing hard on a cigarette, looking out into the fog and acting nervous and jumpy. I leaned against the rail and bowed my head down on my arms. Two or three people standing around there began to look at me. Then, when we were out about a third way in the middle of the stream, I took off my coat that had my name and address written with indelible ink on the label, and my hat that had my initial stamp and goal on the sweatband and laid them down on the deck, climbed up on the rail and jumped. It was as easy as that. A fight with my brother that was loud enough so the house man couldn't help but hear it. A jump off the 23rd Street ferry, leaving plenty of identification behind. An easy swim back to shore where I'd planted my dry clothes and a phone call to the news to report my own suicide. It was just as easy as that. On Friday afternoon, I waited across the street until I saw Williams, the house man leaving for his usual weekend, and then I let myself in the front door and walked back to the study. Come in, Williams. I thought you'd gone. Hello, Walter. What's the matter, Walter? You look as though you'd seen a ghost. Jack, haven't you seen the papers? I thought you were dead. Yeah, I changed my mind. Jack, Jack, how could you? How could you have done such a thing? I didn't. I just went swimming, that's all. Don't tell anyone I'm here. Yes, this is Mr. Parcell. Yes, I told you once it was broken. I'm sure I don't know. I know I certainly didn't do it. Yes, it's still in the box. I'll send you the pieces if you like. Well, that's a little late, I'm afraid. Oh, oh, it doesn't matter anyway. It's the principle of the thing. Besides, I'm going out of town. Yes. Yes, I suppose there will be someone here to receive it. All right. All right. Goldfish bowl. What? You know, I ordered a larger one and derived this morning. All smashed up and they were arguing about sending me a new one. There it is in that big square box you can see for yourself it's smashed. Huh.  At the last minute, you're worrying about a $2 goldfish bowl. What do you mean, the last minute? Well, you just said over the phone you were going out of town. Yes. What's the idea? Well, Jack, I was terribly upset when I heard that, well, when I thought... How bad? Where are you going? Well, I hadn't quite made up my mind. I just wanted to get away. Taking quite a lot of luggage for just a little trip out of town, aren't you, Walter? Clearing the papers out of your desk, too, huh? Uh, yes, I simply thought I... Well, I could get a little work done while I was away. Or were you thinking of staying away for a while because somebody might ask you some questions about why I jumped in the river and the answers might make you look like a heel? Of course not. Such an idea never occurred to me. You always were yellow. You'd run away from anything. Jack, that's quite enough. That's right. Those are the truest words you ever spoke. And I wouldn't bother about packing luggage anymore if I were you. Why not? Because where you're going you won't need any luggage. What do you mean? This is what I mean. Jack! Jack! Don't you joke me! You won't need any luggage anymore, brother. It's like Cain felt about Abel, I suppose. There he was lying on the floor looking as though it was me lying there. Only it wasn't. It was him. And I was glad. It's a funny thing about twins being one yourself. You'd notice them more than most people would. And all the twins I'd ever known had got along good, extra good. But not me and Walter. I hated him ever since I could remember. I hated him because the old man was about the only one who could tell us apart. And it was Walter he always called to him, not me. I hated him for what he got and what I didn't. I hated him because he was always good and I was bad. I hated him because the old man left everything he had to him and it wasn't hey either. Because I couldn't do anything about it. On account of that forgery rap I'd taken. And I hated him for the way he'd taken care of me since I got out of jail and thrown at my face every chance he got. I hated him for all those things and a lot more. And I was dead and I'd killed him. And I was glad. You don't believe me? Brother I felt great. I went over to the mirror and combed my hair over on the left side like his. I locked the study door and went upstairs to the bathroom and shaved off my mustache. He was clean shaven. I went back to the bedroom and put on one of his suits. When I got through and stood in front of the big full length bedroom mirror I looked the spitting image of him. No one in the world could have told that I wasn't Walter Parcell. In fact, I was Walter Parcell. I went back to the study. All I had to do now was dispose of the evidence. But first I couldn't resist looking around. It was mine now. All mine.  In his desk was a list of all the bonds and securities and the number of his safe deposit box and the computation to the safe and the bank book all nice and neat. On the desk was a picture of Helen Winters, the little vixen he was engaged to. I made a mental note that I'd at least have to call her before I left town and it would look funny if I didn't. I might even do more than call her. Well, there's no use stalling any longer. It had to be done. I got the body over my shoulder, carried it upstairs and put it in the bathtub. I locked the bathroom door from the inside. Then I got to work. This is Truman Bradley for Roma Wines. Here's a simple secret about entertaining that has won compliments for many a hostess. The next time you have dinner guests, keep them pleasantly occupied during that hour before the meal by serving Roma California sherry. Serving Roma sherry before dinner has become a friendly American custom. Yes, glorious golden amber Roma sherry with tempting fragrance and intriguing nut-like taste is the perfect first call for dinner. And you'll find Roma sherry equally pleasing with a tasty evening snack, a delightful wine to serve any time. Roma sherry, like all Roma wine, is a true natural wine, crushed from choicest grapes, grown in California's finest vineyards, then unhurriedly, guided to taste perfection by Roma's ancient winemaking skill, bottled at the winery for unvarying goodness. Delight your family, your guests, with delicious Roma sherry. Now selling at the lowest prices in years, insist on Roma, R-O-M-A, for uniformly high quality at low cost. Remember, more Americans enjoy Roma than any other wine. And now Roma wines bring back to our Hollywood soundstage Joseph Cotton as star of the Pasteboard Box, a play well calculated to keep you in suspense. It was early morning before I was able to leave the house. I walked to the nearest subway with a suitcase, a heavy suitcase, because it was also weighted down inside with old furnace grates and sash weights. Got off the subway at Diakman Street and took the Diakman Street ferry to Jersey. About halfway across the suitcase that I had up on the rail as though it was something for me to lean on, just sort of slipped out of my hands into the river.  That was there? About an hour later, the same thing happened on a 42nd Street ferry and the mortal remains of Walter Parcell were gone. All but his head. At first, I had no... What to do with that head? I wouldn't fit into either of the suitcases no matter what I did and then I thought of that box. That big-pace board box that the Goldfish bolded came in was still sitting there in the corner of the desk. I waited it and wrapped up the outside in the paper that if it had come in, it started out again, the 14th Street ferry this time. I had it balanced up there on the rail just like I'd had the others and then... Hey, look out! Oh, that's all right, mister. I've got it. Oh, let go. Oh, I've got it. Hey, what's the matter? Oh, I thought you dropped it. Oh, no. No, here it is. Hey, that was close, all right. Another second and it would have been gone for good. Yeah. It had been gone for good, all right. Walking across 14th Street on the way back from the ferry, people were pushing behind me and the next thing I knew, I was in a department store. I was walking down one of the aisles just to keep moving and not attract attention. When it hit me right between the aisles, there was another box. A box just like mine. I was sitting up there in one of the counters and next to it was an old guy looking at some bow ties. I walked over and put my box on the counter next to his and I pretended I was waiting for the clerk and after a couple of minutes, I pretended to change my mind. I picked up the box, his box, of course, and started for the door. Say, I say there. I say, sir, you've taken my box. What do you mean, your box? Let go of me. But it is. It's my box. You left yours there on the counter.  Let go, I tell you. Why, this man's got my package and won't give it back. Oh, shoplifter, huh? No, no, it's not that. He left a package of his own there, but he insists that mine is his. Now? Apartment lampshade. I bought it at your furniture department just now. The girl confirmed that. What's in yours? Mine? Yes, what's in your box? Why? Oh, they'll open it up and see. No, no, no. You can come over. It's the only way to tell. Open them both up. You think this is your package? No, wait. I made a mistake. It isn't. Here, now give me mine. Just a minute. Just a minute. Can you please? Give it to me. Oh, give it to him. It is. I saw him put it there. Very well. Thank you. Why? He acted like a madman. I guess I did because I was pretty close to panic when I got out of the store. I started walking. I just walked out. I don't know how far, how long, but all I could think of was, what do I do now? What do I do with it? What do I do with it? I didn't snap out of it until I found myself a half a block from home and not knowing how I got there. All I knew was I still had that box and I had to get rid of it. Then I saw the sewer. A corner sewer with a big, wide opening. I crossed over to it as though I was going to step up on the curb. I stumbled. I gave it a good kick. I slid in and I heard it fall. I got home and a half hour later I was just beginning to relax. The doorbell rang. I went out in the hall, switched on the vestibule lights and opened the door. I answered a couple of kids. Yes, this is yours, ain't it, mister? What? We were standing across the street when you dropped it. Then we saw it come into this house. That's how we know. We got some string and a fish hook and pulled it out. It is yours, ain't it? No. You mean it ain't yours? No, I never saw it before in my life. Now beat it. Oh, then we can open it. Hi, Johnny. Wait, no. Here, you give that to me. Give it to me. But you said... I made a mistake. I didn't recognize it. I give it to him. Beat it. Well, aren't you glad to get it back? Oh, sure. Here. It was back. The kids were hardly down the steps before I was out the house without a coat or anything running toward Second Avenue. I didn't care who saw me now. I didn't care a stop for a taxi. I had to keep running. I couldn't stop for a second. I kept on running up Second Avenue to 59th Street. Going out onto the bridge. I was still running and I didn't stop enough. I got nearly to the middle. And then... Then I threw it. Out over the railing as far as I could. I watched it arc down and saw the white splash in the darkness as it hit the water and a couple of hundred feet below. It was gone. No matter what, it was gone. Somehow I got home. But it was daylight before I could get myself to sleep. Monday morning I felt better. I got up fairly early and went down to study and make my plans. Seeing the picture of Helen Winters on the desk reminded me I ought to call her. I had Walter left town without even calling the girl he was supposed to marry. It would look so good. There was no answer. So I hung up. Then I rang for Williams, the house man. Yes, sir? Oh, Williams. I'm sorry to tell you this, but I'm going to have to let you go. I'm sorry to hear it, sir. It's anything I've done. Oh, quite the contrary. I've found our association most pleasant, but the death of my brother has been quite a shock, of course. Of course, sir. I'm going away. I don't know how long I shall be gone or when I shall be back or if I shall come back here at all. So I thought it was best this way. Yes, sir. When will you be leaving, sir? Within a few days. There's no hurry, but I wanted you to be able to make your own plans. I'm making arrangements this afternoon to sell the house and the furniture and the associations here are painful, you understand? I understand, sir. My brother Jack had his faults, of course. We all do. I know how you feel, sir. But after all, Williams, he was my brother. Yes, sir. Blood is thicker than water. You're so right, Williams. That first performance left me feeling pretty satisfied. The next one wasn't so easy. But for things to look right, it had to be done. So after breakfast, I went down to police headquarters. Well, what can we do for you, Mr. Parcell? I'm going away for a while and I wondered if you had recovered my poor brother's... His body? Yes. No, I'm sorry. We haven't, Mr. Parcell. Oh, I see. Now, while you're here, though, there is something you might look at for us. Well... This way, please. It's just a routine matter of identification but we like to have these things on the record, you know. Of course, of course. Something you found... Yeah, that's right. Fished it out of the East River this morning. The East River? That's right. The East River. For a minute, I just stopped breathing because it wasn't the East River that I jumped off the ferry. That was on the other side of the island. The East River was where I'd thrown it. And then I was all right again because I saw what he had. A pair of trousers. Mine. Do you recognize these, Mr. Parcell? Oh, yes. Those are the trousers. My brother wore the night he died. Uh-huh. Probably kicked him off and tried to swim to shore. Probably. Well, thanks, Mr. Parcell. That's all we need. Very well. But you said the East River and it was the North River where Poor Jack... Oh, carried down by the current and around by the tide. Caught in the propeller of a ship, maybe. Funny things happen and the waters around this island, Mr. Parcell? Yes. Yes, I imagine they do. So, that was all right, too. When I got out of headquarters, I went across the street to a play station and phoned Helen Winters again. Then I went uptown to the bank, Walter's Bank. I'd never been in it before in my life and I'd been wondering how I'd know who to be chummy to but I'd needn't have worried about that. I think, Mr. Parcell. Good morning. We were all terribly sorry to hear of your bereavement, Mr. Parcell. Yes, thank you. As a matter of fact, that's what brings me here. I see. Something about the estate? Oh, no, no, no. But I shall want to get into my safe deposit box. Oh, I certainly, Mr. Parcell. Thank you. Oh, by the way, do you happen to know what my cash balance is? Just roughly. Roughly between 32 and 33,000. I'll want 5,000 in cash. I'll make out a counter check. You can forward the rest when I've made banking connections in Mexico. Oh, Mexico? What do you expect to be in Mexico for any length of time? Oh, yes, for quite a length of time. Shall we go down to the vault, sir? Yes, by all means. When I got out of the bank, it was raining, but I didn't care. I liked it. I was walking on air anywhere, and I decided to walk home that way. It's nearly 30 blocks that I was soaking wet when I got there, but what's the little rain to a guy with $100,000 in his pocket? Front door wasn't locked.  And... when I saw it... it... a box. That horrible pace of what box did it come back? For a second I thought my mind had gone, but there it was, sitting on the desk. Wet and soggy in the limp paper peeling office, as though it had been fished out of the river just that minute. And then I remembered I hadn't seen it sink, and what the cop had said about tides and currents. And then the doorbell rang. I rushed to the window. There was a police car outside. For the moment I thought of grabbing up the box and running, escaping out of the bag somehow. And I knew that wasn't any use. It didn't matter. It was some sort of a police plan. It didn't matter anyway. And if it wasn't, if it was just another one of those terrible coincidences, there was still time. Whatever they wanted, I could bluff it through and there'd still be time. I pulled myself together and went out and opened the door. Yes? We're from headquarters. Yes. You're Walter Parcell. Walter Parcell? They thought I was Walter Parcell. They didn't even know he was dead. That was all right. There was still time. I said, are you Walter Parcell? Yes, I'm Walter Parcell. You know a young woman named Helen Winters? Helen Winters, of course. She's my fiance. And I'm afraid you're going to have to come along with us, Mr. Parcell. With who are? Helen Winters has been murdered. And I might as well tell you now that anything you say will be used against you. The evidence is pretty conclusive. That I? That you murdered her. I didn't. I couldn't. We found her this morning in the commoner reports she was killed Friday night. You were seen entering the place that night and you were seen leaving. A gun that we traced to you was found in an ash can a block away. Now what do you expect us to believe, Mr. Parcell? Wait a minute. There's a mistake. There's been a terrible mistake. I'm not Walter Parcell. I'm his brother. I'm his brother Jack. The one who committed suicide? Yes. Only I didn't. I changed my mind. I swam back to shore. I came back here and I found Walter. He was dead. He killed himself. And now I know why. Don't you see? Because he murdered the girl. You didn't report it? Where's the body? The body. Yes, yes, the body, the body. No, that's it. Now look, look, everyone knew I quarreled with Walter and so I thought they'd pin it on me. I thought they'd say I killed him. So, so I disposed of the body. Then I took his place. We are, we're twins, don't you see? Mr. Parcell, I've been in this business a long time and I've heard some beauties. But I never had a man ask me to believe one like that. True. I swear it's true. All right, then where's the body? I threw it in the river with the weights. I thought so. Come on. Now, wait a minute. Come on, come on. I can prove it. I can prove it. Yeah, how? I got his claws because I still got his head. His? His head. That would prove it, wouldn't it? Well, wouldn't it? It certainly would. Come on. I'll show you here in that box, see? I'll open it. Sure, sure. I threw it in the river and it got back here somewhere. It's still wet, see? That doesn't look like anybody's head to me, Mr. Parcell. It's... To me, it looks like just an ordinary goldfish bowl. That was it, of course. The goldfish bowl he'd been arguing about on the telephone when I came back and found him packing up running away because he'd murdered his girlfriend. So, I don't know where Walter is now in those swirling tides and currents, but I know one thing.  Suspense. Presented by Roma Wines. R-O-M-A. Made in California for enjoyment throughout the world. Before we hear again from Joseph Cotton, the star of the Pasteboard Box tonight's suspense play, this is Truman Bradley for Roma Wines. Each day, more Americans are switching to Roma and discovering what a wonderful help Roma Wine is in making simple home entertainment successful. The reason? Taste. Superb taste for only pennies a glass. And, says famous hostess Elsa Maxwell, there's a Roma California wine to delight everyone. Rich, ruby-red Roma port. Mellow, nut-like Roma sherry. Smooth, golden Roma muscatel. And flame-bright Roma toque. I give my guests their choice and share with them Roma's goodness. Each of these fine Roma Wines may be served with cake, fruit, nuts, or other tasty snacks when guests drop in. Many prefer these wines with dessert. You'll find them delightful anytime. Get Roma Wine tomorrow. You'll be amazed how little such taste-luxury costs. For Roma Wine, famed for uniformly fine quality, is now selling at the lowest prices in years. Insist on Roma, R-O-M-A, Roma Wine, made in California for enjoyment throughout the world. This is Joseph Cotton. I've enjoyed my appearance on Suspense as I always do. Next Thursday, an unique actress whom all of us here in Hollywood love and admire, as you do, will be the leading lady on Suspense, Dame Mae Whitty.  I'm sure we'll all want to make it a point to listen. Oh, and by the way, if you feel that the character I played tonight was a little, shall we say, extreme, please forgive me. I've never played twins before, and I guess, well, I guess I just lost my hand. Joseph Cotton appeared through the courtesy of David O. Selznick in whose production, Duel in the Sun, he will soon be seen.  Produced by William Spear for the Roma Wine Company of Fresno, California. This is CBS, the Columbia Broadcasting System.


Hi everyone, Joe for Jaspy's casebrakes.com with another two box break of 2018-2019 upper deck with the Cup Hockey. This is break number 17 right here, chance to win a 1920 OPG Platinum box which is pretty nice if you bought at least two teams. A lot of excellent stuff in here, we'll do that in a separate dice roll at the end of the break. Big thanks to all of these folks for picking their team straight up, appreciate it. No number block or anything like that, nice. Makes things a little bit easier. There you go, thank you. We did pop open a fresh case last break and mark those X's on there so we know they're from the same case. I like that rope die right there. We're going to go 1, 2, 3 for the left side, 4, 5, 6 for the right side. And it's 4, 1, 2, 3, 4, 5, 6, so that's the one we're going to do. This will be for break 18 which is on the website right now, Jaspy's casebrakes.com. We should be able to do those other two tonight, I feel like. I don't think that should be too much of a challenge for us, I think we should be able to do it. All right, good luck. Let's see what we got. A bit of a process there, there you go. Good luck. Good luck. Let's use this blank card right here to slow play some of the hits a little bit. And we've got Bobby Orr, 46 out of 249 for the Bruins, that will be for Karen and Boston. The wrong sized top, the penny sleeves are in there. All right, here we go. Bobby Orr leads us off. We've got Ethan Baer, 201 out of 249, three-color patch and autograph for the Oilers. That'll be for Wade Preston and Edmonton and give you a cracked top, that's not going to be fitting, Ethan Baer, there you go, that's a little bit nicer. There you go, Wade Oilers. And we've got Sean Monahan, signature materials for Calgary, 18 out of 99. That'll be for Scott Corm, in the flames, there you go Scott. We've got Norm Ullman, 86 out of 99 for the Detroit Red Wings. Steve Birch with Detroit. We've got Rasmus Dallin, 92 out of 99, two-color patch, looks like maybe part of a saber in that patch, it looks pretty cool. Buffalo! Stephen Kendrick, Stephen Kay with that one, there you go. And then we've got 243 out of 249, Heinrich Borgstrom for the Florida Panthers and that will be for Solomon, Florida. Alright, next box. Alright, there's Alex Ovechkin, 220 out of 249, Capitals, that'll be for Scott. We've got Morgan Klimchuk, four-color patch, some nice colors in there, and Autograph 218 out of 249 for the Calgary Flames, that's going to go to Scott Corwin. Nice, Scott. We've got Connor McDavid, 5 out of 10, Rookie Auto Patch, it says. I guess we've seen a different version of this, weird throwbacks that they have here. But there you go, that goes to Wade Preston and the Edmonton Oilers, it's a good-looking patch and a nice-looking Autograph out of 10. Game use memorabilia in there too. We've got a little number inscription there as well, nice. We've got Dominique Turzion for the Red Wings, 31 out of 38, that's going to go to Steve Birch. We've got Eric Stahl, 16 out of 33, going to Minnesota, that'll be Joe Drobeck. And we've got Heinrich Borgstrom again for Florida, 146 out of 249. Another two excellent boxes, ladies and gentlemen. Big thanks to everybody who got into the action, really appreciate it. Let's give away a box. McDavid again. It's kind of weird because it still says 18, 19 on the back. They're calling it a Rookie Auto Patch on the front, but still nice. All right, now let's see who's going to win that box. We've got to buy at least two teams. Joe did, so that's an entry, so did Joey. And Joseph bought four, so that'll be two entries. I'm wondering in the house, she has an entry, Michael has an entry, Scott Corwin got four, two entries for him, Solomon is in, Steven Kendrick got three, two count for the purpose of the promo, so that's one entry, SKS got two, so that's an entry, and Steve Birch got four, that's two entries, and Wade got two, that's an entry. Wade can get the Conor McDavid and score a box of an OPG Platinum 2019-2020 edition, could be a Conor McDavid in there too. All right, let me just double check here, Joey, Joseph. Where's Drobak's name? What happened there? I got Joe Klenn, Joey P., Joe Drobak who got four, gets two entries. See, this is why I have to do the double check. And I got Karen, Michael, Scott, Solomon, Steven K., SKS, Birch, Preston. All right, so there's a one spot in 14, he's going to get that sealed box. Let's roll it, let's randomize it, three and a three, six times, hard six. And sixth and final time, name on top is Joey P., there you go Joey, a box of OPG Platinum going your way, congrats to you and thanks everyone for getting in, we've got two more boxes in the shop, go and get it on JazzPieceCaseBricks.com and I'm Joe, I'll bring that with you next time.