Water Pouring Puzzles

Theory

Water pouring puzzles (also called water jug problems, decanting problems, measuring puzzles, or Die Hard with a Vengeance puzzles) are a class of puzzle involving a finite collection of water jugs of known integer capacities (in terms of a liquid measure such as liters or gallons). Initially each jug contains a known integer volume of liquid, not necessarily equal to its capacity.

Puzzles of this type ask how many steps of pouring water from one jug to another (until either one jug becomes empty or the other becomes full) are needed to reach a goal state, specified in terms of the volume of liquid that must be present in some jug or jugs.[3]

By Bézout's identity, such puzzles have solution if and only if the desired volume is a multiple of the greatest common divisor of all the integer volume capacities of jugs.

Problems

  1. How to measure exactly 2 liters of water a) If you have 4 and 5-liter bowls.b) If you have 4 and 3-liter bowls.
  2. Considering three bowls with the following capacities:In bowl A (8 liters capacity), there are 5 liters of water.In bowl B (5 liters capacity), there are 3 liters of water.In bowl C (3 liters capacity), there are 2 liters of water.Can you measure exactly 1 liter, using only 2 pours?
  3. If you need precisely 4 liters of water for your special formula for the award-winning roses during your gardening, but you only have a 5-liter and a 3-liter bowl, and have access to an infinite amount of water, how would you measure exactly 4 liters?

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