Showing what's behind the curtain

Find the smallest prime which, by replacing part of the number with the same digit, is part of an eight prime value set.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order.

Count the values of C(n,r), for 1 ≤ n ≤ 100, that exceed one-million.

Compare hands in a game of poker and determine a winner

Find how many Lychrel numbers are there below ten-thousand.

Considering natural numbers of the form, a^b, find the maximum digital sum.

Investigate the expansion of the continued fraction for the square root of two.

Counting primes that lie on the diagonals of the spiral grid.

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

Find a set of five primes for which any two primes concatenate to produce another prime.