Showing what's behind the curtain

Modified Fibonacci golden nuggets

Count the number of horizontal, vertical and diagonal rectangles in a rectangular grid

Determine if the origin is contained inside a triangle.

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.

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.

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

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

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