12 lts. milk in one can, two measuring cups of 7 and 5 lts, how to get exactly 6 lts?
This puzzle was asked our social group by Devidas Naik. The solution could be written in terms of triplets or 3D vectors (C,S,F): C stands for the can S stands for 7-lt-cup and F for 5-lt-cup. My 11-step/iteration solution goes as $$(12,0,0) \to (5,7,0)\to (4,2,5) \to (10,2,0) \to (10,0,2) \to (3,7,2) \to (3,4,5) \to (8,4,0) \to (8,0,4) \to (1,7,6) \to (1,6,5).$$ Eatlier a 12-step solution was given by Anita Behre that goes as: $$(12,0,0)\to (7,0,5) \to (7,5,0) \to (2,5,5) \to (2,7,3) \to (9,0,3) \to (9,3,0) \to (4,3,5) \to (4,7,1) \to (11,0,1) \to (11,1,0) \to (6,1,5).$$ There could be several other solutions. How to decide the minimum number of steps? Will the minimum step solution be unique? Can we connect this puzzle to some knowm Algorithm, Theorem or Lemma of mathematics?