I found a book with math quizzes. It was my father's when he was young. I encountered a problem with the following quiz. I solved it, but I wonder, is there a faster way to do it? If so, how can I compute the time (polynomial time) that is needed to solve it? Can we build an algorithm?
The problem is this one:
Two brothers have a cow that produces 10 kilos of milk per day. Because they are fair, they share the milk and each one gets 5 kilos.
They only have available three bottles.
$A$ that fits 10 kilos.
$B$ that fits 7 kilos.
$C$ that fits 3 kilos.
How do they share it?
What I did is these steps:
Bottle Sizes A B C 10 7 3 Moves Bottles What we do: 1st 10 0 0 Fill the bottle A. 2nd 7 0 3 Fill the bottle C. 3rd 7 3 0 Empty the index of C in B. 4th 4 3 3 Refill C. 5th 4 6 0 Empty C in B. 6th 1 6 3 Refill C from A. 7th 1 7 2 Refill B from C. 8th 8 0 2 Empty the index of B in A. 9th 8 2 0 Empty the index of C in B. 10th 5 2 3 Refill C from A. 11th 5 5 0 Empty C in B.