Split 8 Litres
Read the puzzle
Three jugs hold 8 litres, 5 litres and 3 litres. The 8-litre jug is full of water and the other two are empty. There is no tap and there are no markings: you may only pour from one jug into another, and a pour stops when the first jug is empty or the second jug is full. The goal is 4 litres and 4 litres. What is the fewest number of pours that does it?
Fewest pours to share it 4 L and 4 L?
Only the 8 L and 5 L jugs can end with 4 L. Use the 3 L jug as a measure.
7 pours
8→5, 5→3, 3→8, 5→3, 8→5, 5→3, 3→8: 4 L and 4 L.
How to solve it
Only the 8-litre and 5-litre jugs can hold 4 litres, so the target is (4, 4, 0), written as (8 L jug, 5 L jug, 3 L jug). The start is (8, 0, 0), and the 3-litre jug works as a measure.
Fill the 5-litre jug first: 8→5 gives (3, 5, 0). Then 5→3 gives (3, 2, 3), 3→8 gives (6, 2, 0) and 5→3 gives (6, 0, 2).
Now the 3-litre jug has room for exactly 1 litre. 8→5 gives (1, 5, 2), 5→3 moves just 1 litre to give (1, 4, 3), and 3→8 gives (4, 4, 0). That is 7 pours.
The usual slip is to start the other way, pouring 8→3 first. That route also works, but it takes 8 pours: (5, 0, 3), (5, 3, 0), (2, 3, 3), (2, 5, 1), (7, 0, 1), (7, 1, 0), (4, 1, 3), (4, 4, 0). Since no route is shorter than 7, the answer is 7 pours.
Takeaway: when two first moves are possible, play both routes out and count; the shorter one wins.
Learn the method: How to Solve Water Jug Puzzles, Step by Step
