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Tips for Water Jars

Solution to the Problem

You should keep one thing in mind: do not make a move that "goes backward" in each and every stage of the game.
For example, when a jar is full and another is half full, you should not pour water out of the half-full jar (since the result can be achieved simply by filling the other jar at the beginning), nor should you pour water into the half-full jar (since the result can be achieved simply by pouring water into the two jars at the beginning).

Therefore, you actually have only one choice at every stage of the game. The following is a solution to the problem:
  1. Fill the 5-liter jar
  2. Pour water from the 5-liter jar to the 7-liter jar
  3. Fill the 5-liter jar
  4. Pour water from the 5-liter jar to the 7-liter jar
  5. Empty the 7-liter jar
  6. Pour water from the 5-liter jar to the 7-liter jar
  7. Fill the 5-liter jar
  8. Pour water from the 5-liter jar to the 7-liter jar
  9. Empty the 7-liter jar
  10. Pour water from the 5-liter jar to the 7-liter jar
  11. Fill the 5-liter jar
  12. Pour water from the 5-liter jar to the 7-liter jar

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