mediumlogic

You have a 5 gallon bucket, a 3 gallon bucket, and a hose to fill them up. You need to get 4 gallons. You have no means of measuring how many gallons are in each bucket (except knowing the bucket capacity). How can you be certain that you have 4 gallons?

Fill up the 3 gallon bucket and pour it in to the 5 gallon bucket (You now have 3 gallons in the 5 gallon bucket). Fill up the 3 gallon bucket again and pour it into the 5 gallon bucket until it is full (You now have 5 gallons in the 5 gallon bucket and 1 gallon in the 3 gallon bucket). Dump the water out of the 5 gallon bucket. Pour the one gallon from the 3 gallon bucket into the 5 gallon bucket (You now have 1 gallon in the 5 gallon bucket). Fill up the 3 gallon bucket and pour it into the 5 gallon bucket. You now have 4 gallons in the 5 gallon bucket.

Why this works

This riddle cleverly uses the concept of measurement through subtraction and transfer between the two buckets. Initially, you fill the 3-gallon bucket and pour it into the 5-gallon bucket, establishing a baseline. By filling the 3-gallon bucket again and transferring until the 5-gallon bucket is full, you effectively measure out 1 gallon remaining in the 3-gallon bucket. When you dump the 5-gallon bucket and add that 1 gallon back in, you create a known quantity in the larger bucket. Filling the 3-gallon bucket again and pouring it into the 5-gallon bucket then gives you exactly 4 gallons in total, showcasing how you can measure indirectly through the process of filling and emptying!

Common Wrong Answers

“Fill the 5 gallon bucket completely and then try to measure out 4 gallons from it.”

This method does not involve measuring or using the 3 gallon bucket effectively, which is necessary for achieving exactly 4 gallons since there's no way to remove water from the 5 gallon bucket without spilling or measuring.

“Just fill up the 5 gallon bucket and then pour out 1 gallon.”

There is no way to pour out exactly 1 gallon from the 5 gallon bucket without a measuring tool, so this method cannot guarantee that you end up with exactly 4 gallons.

“Fill the 3 gallon bucket twice and pour it into the 5 gallon bucket.”

Filling the 3 gallon bucket twice would give you 6 gallons, which exceeds the capacity of the 5 gallon bucket, and you cannot measure out or retain only 4 gallons this way.

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