The Three Vessels of the Sage belongs to the great tradition of problems that seem narrative and turn out to be exact. It preserves that ancient flavor in the statement, but requires a precise sequence that does not allow trial and error.
The three vessels of the wise man (ancient India)
Riddle statement
A wise man has three vessels of 12, 8 and 5 liters. The 12 is full; the other two are empty.
You must divide the content into two equal parts, using only transfers between vessels and without intermediate marks.
How do you do it?
Show solution
Solution
Answer: Yes. It is achieved in 7 transfers, ending with two containers of 6 liters.
Sequence of states $(12L, 8L, 5L)$:
$(12,0,0) \to (4,8,0)$ $(4,8,0) \to (4,3,5)$ $(4,3,5) \to (9,3,0)$ $(9,3,0) \to (9,0,3)$ $(9,0,3) \to (1,8,3)$ $(1,8,3) \to (1,6,5)$ $(1,6,5) \to (6,6,0)$
The key is in the intermediate steps: the pot of 5 acts as an auxiliary measure to break the initial symmetry and force the remainder 1 that appears in step 5. That "lone 1" in the pot of 12 is the pivot from which the exact partition is constructed in the final two transfers.