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Making Change: Ground Rules

Making Change: Ground Rules. For the sake of the puzzles in this presentation: Coin means one of the pieces 1¢, 5¢, 10¢, 25¢ (no 50¢ or $1 coin) Bill means one of the denominations $1, $5, $10, $20, $50, $100.

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Making Change: Ground Rules

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  1. Making Change: Ground Rules For the sake of the puzzles in this presentation: Coin means one of the pieces 1¢, 5¢, 10¢, 25¢ (no 50¢ or $1 coin) Bill means one of the denominations $1, $5, $10, $20, $50, $100 Warm-up puzzle: What is the largest sum of coins that you can have in your pocket without being able to make exact change for $1? Satisfiability

  2. Diophantineequation Count the number of integer solutions to the equation 25Q + 10D + 5N + P = 100 The Many Ways of Making Change In how many distinct ways can you make change for $1? Satisfiability

  3. Is there a solution to 25Q + 10D + 5N + P = 100 that satisfies the constraint Q + D + N + P = 22? Making Change with Constraints Can you make change for $1 using exactly 22 coins? Satisfiability

  4. 7 –8 –8 9 –8 –8 –9 2 –9 3 –8 –8 7 3 –5 5 –7 –8 –8 –8 –8 2 –7 6 –2 –5 –4 9 –6 8 1 2 –4 9 6 The Satisfiability Game Pick one of the numbers shown in the table (say x) Color all boxes containing x green (or circle it) and all boxes containing –x red (or X it out) You win if every row has a green box (circle) You lose if some row has three red boxes (Xs) Play the satisfiability game on-line at the following website. The game has five difficulty levels. http://www.cril.univ-artois.fr/~roussel/satgame/satgame.php?level=1&lang=eng Satisfiability

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