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