This was just a mirrored text. Answer: FIRST


The text is written backwards. The division into 5-letter blocks had no meaning whatsoever. Answer: NUMBER


The first letters of the words give the solution. Answer: EQUAL


Caesar shift by 4. Answer: TO


The alphabet has been reversed. That is, the letters were substituted according to: a <-> z, b <-> y, c <-> x, … Answer: ITS


If one marks the cities on the map and joins the dots in the given order, he will obtain a shape - crown. You only needed to write down ‘Crown’ onto the underscores and submit the red part (the last three letters). Answer: OWN


The k-th power of boundary operator ‘removes’ the first k letters from the following picture. That is, if you had a picture of a cat and this was preceded by a boundary operator to the second power, you are left with ‘T’. Answer: PARTS


Quite clearly, the question is: ‘First number equal to its own parts’. What is ‘number equal to its own parts’? Euclid says in his elements: A perfect number is that which is equal to its own parts. That is, you only had to give the first perfect number. Answer: 6


Vigenere cipher with key NINE. Answer: TORUS


This is nothing else than the flag semaphore alphabet. Answer: 8191


Counting the number of legs touching the ground in each picture gives a letter. Answer: DETERMINANT


A very simple version of the transposition cipher. The only thing that one needed to do was to swap letters in consecutive pairs of letters. Answer: ELEMENTS


One could have noticed the regularity in the numbers. The solution was to partition every row into perfect squares. Then the number in the parantheses only gave a number of squares/letters to be found in each row. Answer: ERDOS


The upper parts of roman numerals. Answer: OLIVER


One-time pad. This was a little bit tricky - one had to remember the string of letters of equal length than this one, that appeared on the cipher hunt posters. Upon subtracting these two, one obtains the answer: CONGRATSTORETREIVETHEPRIZEMESSAGEUSYOURFAVOURITEMATHEMATICIAN