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Chapter 7: Problem 53

Using just a five-gallon bucket and a three-gallon bucket, can you put four gallons of water in the five-gallon bucket? (Assume that you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

Short Answer

Expert verified
Answer: To measure exactly four gallons of water, follow these steps: Fill the three-gallon bucket completely and pour it into the five-gallon bucket. Fill the three-gallon bucket again and pour it into the five-gallon bucket until full, leaving 1 gallon in the three-gallon bucket. Empty the five-gallon bucket and pour the remaining 1 gallon from the three-gallon bucket into it. Finally, fill the three-gallon bucket again and pour it into the five-gallon bucket, resulting in exactly four gallons of water.

Step by step solution

01

Fill the three-gallon bucket

Fill the three-gallon bucket completely with water.
02

Pour the three-gallon bucket into the five-gallon bucket

Carefully pour all the water from the three-gallon bucket into the five-gallon bucket. Now, the five-gallon bucket has 3 gallons of water.
03

Fill the three-gallon bucket again

Fill the three-gallon bucket completely with water once more.
04

Pour the three-gallon bucket into the five-gallon bucket until full

Pour the water from the three-gallon bucket into the five-gallon bucket until the five-gallon bucket is full. Since there are already 3 gallons of water in the five-gallon bucket, you will only be able to pour 2 more gallons into it. This will leave 1 gallon of water in the three-gallon bucket.
05

Empty the five-gallon bucket

Now, empty the entire five-gallon bucket, leaving it with zero gallons of water.
06

Pour the remaining water from the three-gallon bucket into the five-gallon bucket

Pour the 1 gallon of water left in the three-gallon bucket into the empty five-gallon bucket. The five-gallon bucket now has 1 gallon of water.
07

Fill the three-gallon bucket again

Fill the three-gallon bucket completely with water once again.
08

Pour the three-gallon bucket into the five-gallon bucket

Pour all the water from the three-gallon bucket into the five-gallon bucket, which already contains 1 gallon of water. This will result in a total of 4 gallons of water in the five-gallon bucket (1 gallon already inside + 3 gallons from the three-gallon bucket). You have now successfully measured 4 gallons of water in the five-gallon bucket.

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