Showing what's behind the curtain

Finding Nim positions consisting of heap sizes n, 2n and 3n for n ≤ 2^{30} that result in a losing game.

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

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

Rooms of Doom

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