How many transactions can you calculate?

Logic Level 3

A maid was sent to the brook with two vessels that exactly measured 7 7 pints and 11 11 pints, respectively. She had to bring back exactly 2 2 pints of water. What is the least number of transactions necessary?

Notes:

  1. A "transaction" is filling a vessel, or emptying it, or pouring from one vessel to another.

  2. The last transaction is when there is exactly 2 2 pints of water in any of the vessels.

14 8 5 20 It is not possible to have 2 2 pints of water. 10 16

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