In a perfect shuffle a deck of cards is divided exactly in half, which are interleaved alternately together. This can be done two ways: In an in-shuffle the bottom half is interleaved on top (1234 5678 → 51627384) and in an out-shuffle the top half is interleaved on top (1234 5678 → 15263748). Take an ordinary deck of 52 cards and sort it into a recognizable order. Do consecutive out-shuffles for the deck and observe how the order changes (alternatively, if you feel more agile, write a computer program that simulates the shuffling). What happens eventually

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.