If you have a twelve gallon bucket, a seven gallon bucket, and a six gallon bucket, how can you get exactly nine gallons into one bucket
Completely fill the 7 gallon bucket.
Pour the water from 7 gallon bucket into 12 gallon bucket.
Again completely fill the 7 gallon bucket.
Pour the water from 7 gallon bucket into 6 gallon bucket.
Now in 7 gallon bucket you have 7 - 6 = 1 gallon.
Pour that 1 gallon into 12 gallon bucket.
Now in 12 gallon bucket you have 7 + 1 = 8 gallons.
Pour the water from 6 gallon bucket into 7 gallon bucket.
Now in 7 gallon bucket you have 6 gallons.
Completely fill the 7 gallon bucket.
Again pour the water from 7 gallon bucket into 6 gallon bucket.
Again in 7 gallon bucket you have 7 - 6 = 1 gallon.
Pour that 1 gallon into 12 gallon bucket.
Now in 12 gallon bucket you have 7 + 1 + 1 = 9 gallons.
There are a lot of ways doing these. Mine might be a long way, there might be a shorter way. Anyway, let the contents of each gallon be represented in this format:
(12-gallon bucket) - (7-gallon bucket) - (6-gallon bucket)
Fill the 12-gallon bucket. Leave the others empty. So:
12 - 0 - 0
Put the 12 gallon to the 7-gallon bucket. Remaining gallons in 12-gallon bucket is therefore 5:
5 - 7 - 0
Put the 7 gallon in 6-gallon bucket. Remaining gallons in 7-gallon bucket is therefore 1:
5 - 1 - 6
Put the 6 gallons from 6-gallon bucket to 12-gallon bucket:
11 - 1 - 0
Put the 1 gallon to 6-gallon bucket:
11 - 0 - 1
Put the 11 gallons to 7-gallon bucket. Remaining gallons in 12-bucket is therefore 4:
4 - 7 - 1
Discard the contents of 6-gallon bucket:
4 - 7 - 0
Put the 4 gallons to 6-gallon bucket:
0 - 7 - 4
Fill the 12-gallon bucket:
12 - 0 - 4
Put the 12 gallons to 7-gallon bucket. Remaining gallons in 12-gallon bucket is therefore 5:
5 - 7 - 4
Finally, put the 4 gallons from the 6-gallon bucket to 12-gallon bucket:
9 - 7 - 0
hope this helps~ `u`
To get exactly nine gallons into one bucket using a twelve-gallon bucket, a seven-gallon bucket, and a six-gallon bucket, you can follow these steps:
1. Fill the twelve-gallon bucket completely.
2. Pour the contents of the twelve-gallon bucket into the seven-gallon bucket until it is full, leaving five gallons in the twelve-gallon bucket.
3. Empty the seven-gallon bucket.
4. Pour the remaining five gallons from the twelve-gallon bucket into the six-gallon bucket.
5. Fill the twelve-gallon bucket again.
6. Pour water from the twelve-gallon bucket into the six-gallon bucket until it is full, which will leave three gallons in the twelve-gallon bucket.
7. Empty the six-gallon bucket.
8. Pour the three gallons from the twelve-gallon bucket into the empty six-gallon bucket.
9. Fill the twelve-gallon bucket for the third time.
10. Pour water from the twelve-gallon bucket into the nine-gallon bucket until it is full, which will leave exactly nine gallons in the twelve-gallon bucket.
Following these steps will allow you to measure out precisely nine gallons using the given buckets.