Showing what's behind the curtain

Which base/exponent pair in the file has the greatest numerical value?

Using a brute force attack, can you decrypt the cipher using XOR encryption?

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

Determining the number of solutions of the equation x^{2} − y^{2} − z^{2} = n.

Finding the number of blue discs for which there is 50% chance of taking two blue.

Find the smallest prime which, by changing the same part of the number, can form eight different primes.

Compose Champernowne’s constant

Investigate the game of chance involving coloured discs.

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

Find a quadratic formula that produces the maximum number of primes for consecutive values of n.