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Measuring four gallons with 5- and 3-gallon jugs

Question

You have an unlimited water supply, an unmarked 5-gallon jug and an unmarked 3-gallon jug. How can you end up with exactly 4 gallons?

Short answer

Fill, pour, empty, repeat. Fill the 5, pour into the 3 (leaving 22 in the 5), empty the 3, pour the 22 gallons into the 3, refill the 5, then top up the 3 (which needs just 11 gallon), leaving exactly 44 gallons in the 5. It works because 4=2⋅5−2⋅34=2\cdot5-2\cdot3, an integer combination of the jug sizes.

Adapted from Crack, Heard on the Street, Q5.5.13, p.55; question and answer rewritten by SelfMadeQuant.com.

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