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A hundred animals for a hundred pounds

numbersdiophantinemodular-arithmeticclassic

At a market, horses cost 10 pounds each, goats cost 1 pound each, and ducks are sold in bunches of 8 for 1 pound.

Buy exactly 100 animals for exactly 100 pounds, with at least one of each kind. Ducks must be bought in whole bunches. Find the combination and show it is the only one.

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Write two equations, one for the count and one for the cost, and eliminate the goats. You will be left with a single equation in horses and ducks whose whole-number solutions are easy to find by looking at remainders.

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Chinese Remainder PuzzlesFermat's Little Theorem in PuzzlesInvariants and MonovariantsAdaptive Versus Pre-Committed Weighing StrategiesThe Lost Boarding Pass Problem

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