Three jugs are given, each containing an integer amount of pints of water. It is allowed to pour in any jug as much water as it already contains, from any other jug with a greater amount of water. Prove that after several such pourings it is possible to empty one of the jugs. (Assume that the jugs are sufficiently large; each capable of holding all the water available.)
Friday, February 4, 2011
3 Jugs Problem - A Water Doubling Variant
Problem :
Three jugs are given, each containing an integer amount of pints of water. It is allowed to pour in any jug as much water as it already contains, from any other jug with a greater amount of water. Prove that after several such pourings it is possible to empty one of the jugs. (Assume that the jugs are sufficiently large; each capable of holding all the water available.)
Three jugs are given, each containing an integer amount of pints of water. It is allowed to pour in any jug as much water as it already contains, from any other jug with a greater amount of water. Prove that after several such pourings it is possible to empty one of the jugs. (Assume that the jugs are sufficiently large; each capable of holding all the water available.)
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