Showing what's behind the curtain

Integer partition equations

Find how many 18-digit numbers (without leading zeros) there are such that no digit occurs more than three times in base 10.

Find the number of triangles present in a cross-hatched triangle of size n.

Maximizing a weighted product

Counting the number of consecutive nines at the beginning of the fractional part of (√p+√q)^{2n}

Find the volume (in m^{3}) of the region through which the fragments of an air-burst firecracker move before reaching the ground.

Find the number of factors in an enormous factorial.

Project Euler 183: Find the maximum product of equal parts of a number and determine whether the that product is a terminating or non-terminating decimal .

Find the expected number of plates that must be observed to find two that total 1,000.

Modified Fibonacci golden nuggets