The Pigeonhole principle is a useful tool that can be applied in various scenarios. Applying this principle, one can perform data integrity checks and make statistical predictions.

Nim’s game is played with a set of heaps, each containing a certain number of objects or stones. Two players take turns removing objects from the heaps

Given a function foo(), that returns an integer between 1 and 5 with equal probability. Write a function using foo() that returns an integer between 1 and 7.

Consider the 2D grid formed by integer points on the XY Plane. The position of the Sniper and the Target are lattice points in this grid. The bullet shot by the Sniper will follow a straight line trajectory from (x1, y1) to (x2, y2). The bullet goes no further than (x2, y2).