Problem: Placing Halfpennies


Here is an interesting little puzzle suggested to me by Mr. W. T. Whyte. Mark off on a sheet of paper a rectangular space $5$ inches by $3$ inches, and then find the greatest number of halfpennies that can be placed within the enclosure under the following conditions. A halfpenny is exactly an inch in diameter. Place your first halfpenny where you like, then place your second coin at exactly the distance of an inch from the first, the third an inch distance from the second, and so on. No halfpenny may touch another halfpenny or cross the boundary. Our illustration will make the matter perfectly clear. No. $2$ coin is an inch from No. $1;$ No. $3$ an inch from No. $2;$ No. $4$ an inch from No. $3;$ but after No. $10$ is placed we can go no further in this attempt. Yet several more halfpennies might have been got in. How many can the reader place?

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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