Coin touches coins

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?




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Henry has been caught stealing cattle and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.

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In Canada, a mathematical puzzle must be solved in order to win the lottery to classify it as a “game of skill” not gambling.