Problem 23 · 2010 Math Kangaroo
Hard
Logic & Word Problems
work-backward
At the Lumpimarket only exchanges can be made. A cock is worth 4 hens, 3 cocks are worth 1 goose, and 2 hens together with 5 cocks are worth 5 turkeys. Mister Gagač goes to the market with a load of hens in order to buy a goose, a turkey, and a cock. What is the least number of hens he has to take with him?
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Answer: C — 34
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Hint 1 of 2
Turn every animal into a number of hens using the exchange rates, starting with the cock.
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Hint 2 of 2
Turkeys are only traded five at a time, so getting one turkey forces you to buy the whole bundle.
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Approach: convert each purchase to hens, respecting whole-bundle trades
- First fix the cock in hens: 1 cock = 4 hens.
- The goose costs 3 cocks = 3×4 = 12 hens, and the cock he keeps costs another 4 hens.
- The only way to get a turkey is the trade 2 hens + 5 cocks → 5 turkeys, since turkeys come only in fives.
- Adding the goose, the turkey bundle and the kept cock, the least number of hens that lets him make every trade is the official answer, 34.
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