Langton’s Ant moves on a grid of squares that can be either black or white. The grid begins as fully white and the ant can only face left, right, down or up. It then moves in accordance to the following two rules:

If the ant is on a black square, it changes the colour of the square to white, rotates 90 degrees anticlockwise and moves forward one square.

If the ant is on a white square, it changed the colour of the square to black, rotates 90 degrees clockwise and move forward one square.

Find the total number of black squares on the grid after the ant moves 1000 times.

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A Square Triangular Number is number which is both triangular and a perfect square (36 for example). Find the sixth Square Triangular Number (including 1, but excluding 0).

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The Reddo is a new currency, which comes in coin denominations of all the prime numbers less than twenty. For example, 10 Reddos can be made with five combinations of coins:

Find the number of combinations in which 50 Reddos can be made.

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Find the number of years between 0 AD to 2014 AD that have began (on the 1st January) on a Monday.

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For the purposes of this problem the characters of the string “Contest Coding” are assigned values, the value assigned to a particular character determined by the position in the string of that character – viz:

That sequence of values is considered the 1^{st} lexicographic permutation; given the characters to which those values are assigned, what n^{th} lexicographic permutation will first contain the sequence of characters “tsetnoC”?

– This puzzle was suggested by Mark Bishop

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To convert between bases, follow the instructions at this website. When using base 36, all the digits 0-9 and all the letters A-Z are used. Find the decimal (base 10) equivalent of the base 36 number “CONTESTCODING”.

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