Showing what's behind the curtain

Find the 2000th hexagonal tile in which the differences between it and its 6 neighbors yield 3 primes.

Find the sum of the perimeters of all *almost equilateral triangles* with integral side lengths and area.

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

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

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 ways a row measuring fifty units in length could be filled with blocks three units long. 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, heterogeneously, measuring 2, 3 or 4 units long.

Find how many Pythagorean triangles allow tiling with a perimeter < 100,000,000.

The prime factorisation of binomial coefficients

Powers With Trailing Digits