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A problem with bowling

A problem with bowling

Ten equal coins are placed in the same triangular formation with which bowling is arranged.

What will be the minimum number of coins to withdraw so that no equilateral triangle of any size can be built with the remaining centers?

Solution

The minimum number of coins to withdraw is four as shown in the picture Thus, you can never take three centers of the remaining coins that are at the vertices of an equilateral triangle.

Except for rotation, the configuration of the coins is unique and identical to its symmetric.