Question

You have a 45-gallon jug and a 124-gallon jug. neither of the jugs has any markings (although you do know their capacities). describe a way to measure exactly one gallon of water.

Answer 1

4*124 = 496
11*45 = 495

Fill the 124-gallon jug 4 times, emptying it each time into the 45-gallon jug. After the 45-gallon jug has been filled 11 times, there will be 1 gallon remaining in the 124-gallon jug.

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Mathematically, this works fine. In practice, you're looking for a 1-gallon difference after handling 495 gallons of water. That's about 0.2% of the total amount of water transferred. Any error along the way will substantially affect the outcome.

Answer 2

Pour 4  times of 124-gallon into a big jug.
Amount of water = 124 x 4 = 496 gallons

Then use the 45-gallon jug to scoop out the water 11 times.
Amount of water scooped out = 11 x 45 = 455 gallons

Water remaining = 496 - 450 = 1 gallon.