Puzzle of the week

How can you construct a plane where every point is coloured either black or white such that two points of the same colour are never a unit distance apart?


Previous puzzle

Alex and Bob work as financial advisors for the same company. They draw equal salaries from the company. They behave well at the office. Both work on similar assignments. Each assignment requires a yes-no decision. The company uses the decisions made by them to make profits.

After the recession hit the company very badly, one of them has to be fired. Both Alex and Bob have worked on almost the same number of assignments in the last ten years. Alex has been consistently taking about 80% decisions correctly every year. Bob, on the other hand, has been taking only about 5% correct decisions every year.

Assuming that the performances of Alex and Bob would remain the same in future, who should the company fire to maximize its profits in the years to come? Why?


Random puzzle from the past

There are 64 pawns placed on a chessboard. Each square contains a pawn. Two squares are neighbours of each other if they share a common side.

In the first step, some pawns are removed. Then, at every step thereafter, a pawn is removed from any square with at least two empty neighbours. This continues until the board is empty or no more pawns can be removed.

What is the minimum number of pawns that must be removed in the first step so that all pawns can be removed in the subsequent steps?


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