How do you measure 1 gallon in a 4 gallon vat?

Answer 1

It is impossible to measure out exactly 1 gallon into a 4 gallon container, unless the container has appropriate markings for measurement. However, if you had a 2nd container available, it may be possible to derive a 1 gallon measurement. Assuming a 2nd container of size:

1 Gallon:

Just use the 2nd container

2 Gallon:

Impossible

3 Gallon:

Fill the 4 gallon container completely, then pour it into the 3 gallon container until full. You should have exactly 1 gallon left in the 4 gallon container.

4 Gallon:

Impossible

5 Gallon:

Fill the 5 gallon container until it is full, then dump it's contents into the 4 gallon container, leaving exactly 1 gallon left in the 5 gallon container.

6 Gallon:

Impossible

7 Gallon:

Fill the 4 gallon container completely, then empty it's contents into the 7 gallon container. Repeat this process, and when the 7 gallon container is full, there should be exactly 1 gallon left in the 4 gallon container.

8 Gallon:

Impossible

9 Gallon:

Fill the 9 gallon container completely, then use it to fill the 4 gallon container. Once the 4 gallon container is full, empty it and repeat. After pouring from the 9 gallon container twice, you will end up with exactly 1 gallon left.

10 Gallon:

Impossible

This pattern repeats for all containers that satisfy the following equations:

C*n+1

C*n-1

Where C is the size of the original container (4 in this case), and n is all whole numbers greater than 0. The only additional case would be a 2nd container size of 1.