Many Jugs to One I
This is a problem from a Bulgarian 1989 winter competition. The proof below, by Miroslav Petkov, was awarded a special prize.
References
- S. Savchev, T. Andreescu, Mathematical Miniatures, MAA, 2003
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Proof
Assume on the contrary that n = 2km, where m > 1 is odd. Choose such an initial distribution of water as to have every jug contain a multiple of 2k. It is always possible by, say, having 2k in one jug and
making m even. A contradiction.
(The problem admits a converse.)
- The Three Jugs Problem. Introduction and a story
- 3 Glasses Puzzle
- Water puzzle, experimental math
- Three Glass Puzzle (Graph Theoretical Approach)
- The puzzle in barycentric coordinates
- Two Pails Puzzle
- Plain Gadgets
- 3 Jugs Problem - A Water Doubling Variant
- Many Jugs to One I
- Many Jugs to One II
- Three Jugs - Equal Amounts
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Copyright © 1996-2018 Alexander Bogomolny
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