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Mobius Strips and the Six-Color Map Theorem [12/16/1998]
An extension of the four-color map theorem to the mobius strip, i.e. the six-color map theorem.

Average Age at a Party [10/27/1999]

Bell Numbers [08/29/2001]

Binary Search Trees [02/06/2003]
Which of the following sequences represent(s) an order of insertion that will result in a binary search tree where each node in the tree has the same number of nodes in its left and right subtrees?...

Breadth-First Search and Girth [11/13/2000]
How can you use a breadth-first search to compute the girth (length of shortest cycle) of a graph?

Checkerboard Chase [12/13/2002]

Circle Chords [11/4/1994]
Place n distinct points on the circumference of a circle and draw all possible chords through pairs of these points. Assume that no three of these chords pass through the same point. Find and solve the recurrence relation for the number of interior intersection points formed inside the circle.

Climbing 100 Steps [05/01/2003]
Find the number of ways in which you can climb 100 steps if you can go up 1 or 2 steps at a time.

Condorcet Criterion [02/13/2002]
Please explain the "Condorcet candidate" when using various ways to determine a winner in an election.

Covering a Checkerboard after Removing a Random Square [05/11/2008]
Use mathematical induction to prove that for any positive integer n, if any one square is removed from a 2^n x 2^n checkerboard, then the remaining squares can be completely (and exactly) covered with L-shaped pieces composed of three squares.

Creating a Payoff Matrix [06/04/2003]
Shoe Town and Fancy Foot are both vying for more share of the market.

DeBruijin Diagrams/Shift Register Graphs [10/30/2001]
My specific problem is how to graph D(3,3) and then come up with a shift register sequence from that graph.

Dinner Triplets [10/23/2000]

Elect a Spokesman [07/02/2002]
The 23 prisoners and the 'switch room.'

Equivalence Relations [02/10/2003]
For integers m and n, define m~n if n|m^k and m|n^k for some positive integers j and k.

Finding Formulas for Number Sequences [11/22/1997]
My question is about trying to find a formula between numbers.

Finding Pairs of Intersecting Chords [07/24/2000]
Consider n chords on a circle, each defined by its end points. Describe an O(n*ln(n)) algorithm for determining the number of pairs of chords that intersect inside the circle.

Finding the nth Term [03/28/2002]
My formula works with the exception of the first term.

Four-Color Map Theorem [4/3/1995]
I hear the Four-color map theorem was either proved or disproved and that extensive computer effort was required....


Generating Eight-Character Passwords [03/08/2002]


Graph Theory [02/25/1997]
Prove that the maximum number of edges in a graph of order n without an even cycle is [3/2(n-1)].


How Many Distinct Patterns? [01/15/2001]

The Hungarian Job Assignment [03/10/2011]

Induction Hypothesis [08/16/2003]
Every road in Sikinia is one way. Every pair of cities is connected by exactly one direct road. Show that there exists a city which can be reached from every other city either directly or via at most one other city.


Inverse, Product of Permutations [04/27/2002]

Karnaugh Maps [05/07/2000]
What are Karnaugh maps? How are they used?

The Königsberg Bridge [5/20/1996]
Do you have information on Konigsberg's bridge?

Matching Invoices with Report Totals [10/31/2000]
I have 14 invoice values and 2 report totals. The sum of the invoices for each report should be the report total. Is there a fast way of finding which invoices go with each report, or determining if it is even possible?


Maximizing the Number of Rectangles [10/26/2000]
How can I cut a rectangular sheet of paper into a maximum number of smaller rectangles of a given size? Is there an algorithm for this?

Maximum Area Given Enclosing Lengths [11/21/2001]


No Three Red Beads Together [09/16/2001]

Number/Color Cube [09/13/2001]

Numbers Identical in Base 10 and Base 3 [02/14/2001]
Find all base-10 numbers that, when multiplied by eight, have exactly the same digits as their base-3 counterparts.

Numeric Combinations of Pi and Sqrt(2) [09/25/2005]
Say I am given a number X = A*[sqrt]2 + B*[pi], where A and B are integers. For a given X, how can you find A and B?

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