The math inside

Penny Wise

Rules

1 1 1 1 ×4 5 5 5 ×3 10 10 ×2 25 ×164¢ 1
Everyone starts the same, every coin in plain sight
1 5 25 5 1 1 5 10 Table 2
On your turn, put one coin in the middle of the table
10 5 1 1 7 < 10 10 5 5 10 = 10 3
Then take back change worth less; less or none is fine
5 1 Out 10 4
Out of coins means out; your turns are skipped

The last player still holding coins wins.

Where it comes from, and questions to think about

James Ernest designed this game, and Ben Orlin includes it in Math Games with Bad Drawings. Put a coin down, take back a little less. Making change happens every day, yet it hides real math. Why must the game end? And why are coins 1¢, 5¢, 10¢ and 25¢ anyway? Pennywise, Math with Bad Drawings

Questions strong players ask

  • Under 99¢, which amount needs the most coins to make?
  • If you could redesign the four coins, which four would make every amount from 1¢ to 99¢ with the fewest coins in total?
  • Try "perfect change": you must take back exactly 1¢ less than you put down. Or looser: you may take back as much as you put down. Could either game go on forever?
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