Showing what's behind the curtain

Fill an empty row with blocks, a minimum length of 50 units, until the size of the row exceeds 1,000,000 units. The blocks must be separated by at least one empty space.

Count the number of ways a space 50 units long could be filled by tiles, homogeneously, measuring 2, 3 or 4 units long.

Count the number of ways a space 50 units long could be filled by tiles, heterogeneously, measuring 2, 3 or 4 units long.

Investigating the numbers which are equal to sum of their digits raised to some power.

Find the value of the first triangle number to have over five hundred divisors

Finding the maximum remainder when (a − 1)^{n} + (a + 1)^{n} is divided by a^{2}.

Investigate the game of chance involving colored discs.

Find the maximum remainder when (`p` − 1)^{n} + (`p` + 1)^{n} is divided by `p`^{2} for prime `p`.

Find the kth element in a sorted list of radicals.

Finding square sums that are palindromic.