# Amazon Supposedly Asked Interview Candidates to Solve This 'Chess Board' Puzzle

Philip Ellis

Tech giants like Google, Facebook and Amazon are reportedly quite keen on presenting candidates with all kinds of puzzles, brainteasers and logic games during the interview process, in order to find out how people think and approach problem-solving. A recent video on the Logically Yours channel breaks down one such example, a probability-based puzzle reputed to have been used by Amazon.

The setup is simple. A coin, with a diameter measuring 1, is thrown onto an infinitely large chessboard where each square has sides that measure 2. What are the chances of the coin touching both black and white colours when it lands on the board?

The coin will enclose two colours if crosses one or two sides of a square. It will only touch one colour if it doesn't cross any of the sides. If it touches a side, but doesn't cross it, it still only covers one colour.

Here's how to work it out.

The centre of the coin, the video explains, is what decides if the coin crosses a side or not. By moving the coin around the sides of the square, and tracing the movements of the centre of the coin, you get the boundary limit for the coin's centre in the form of a smaller, inner square. This represents the maximum limit in which the coin will only touch one colour. In other words, if the coin's centre were to land anywhere inside that inner square, it would only touch one colour. If it lands outside that, it will cross one or more sides and touch both black and white.

That outside section is equal to the area of the main square, minus the area of the inner square. To calculate the area of the inner square, subtract the circle's radius (0.5) from the the main square's length (2) twice. In other words, 2 minus 1. Then square it; the inner square has an area of 1. The main square has an area of 4. That means the rest of the square has an area of 3 (4 minus 1).

The probability that the coin will land outside the inner square is: outside area divided by whole square area: in other words, 3/4 or 75 percent.

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