Using Your Brain

At a rural cabin, you get water from a well using only a 4-gallon bucket and a 9-gallon bucket. In a single trip from the well to the cabin, what whole number gallon amounts of water could you bring back to the cabin?

There are no markings on the pails.  And, you can’t do any estimating or add any markings!

1- Fill up the 9 gallon bucket, then pour 4 gallons onto the 4 gallon bucket twice and what ever is left over has to be 1 gallon because you started with 9 gallons.

2- Fill up the 9 gallon bucket, then pour 4 gallons onto the 4 gallon bucket twice and what ever is left over has to be 1 gallon because you started with 9 gallons pour the 1 gallon onto the 4 gallon bucket. Then fill up the 9 gallon bucket again leaving you with 10 gallons. Then Fill whatever is left from the 4 gallon bucket leaving only 6 gallons on the 9 gallon bucket. Then fill up the 4 gallon bucket by pouring some out of the 9 gallon bucket then dump the 4 gallon bucket leaving you with 2 gallons.

3- Fill up the 4 gallon bucket and dump it in the 9 gallon bucket twice. Then fill up the 4 gallon bucket and fill up whatever is left to fill from the 9 gallon bucket then dump the 9 gallon bucket and whatever is left from the 4 gallon bucket is 3 gallons.

4- Fill up the 4 gallon bucket

5- Fill up the 9 gallon bucket.  Pour 4 gallons into the 4 gallon bucket leaving 5 gallons in the 9 gallon bucket.

6- Fill up the 9 gallon bucket, then pour 4 gallons onto the 4 gallon bucket twice and what ever is left over has to be 1 gallon because you started with 9 gallons pour the 1 gallon onto the 4 gallon bucket. Then fill up the 9 gallon bucket again leaving you with 10 gallons. Then Fill whatever is left from the 4 gallon bucket leaving only 6 gallons on the 9 gallon bucket.

7- Fill up the 4 gallon bucket and dump it in the 9 gallon bucket twice. Then fill up the 4 gallon bucket and fill up whatever is left to fill from the 9 gallon bucket then dump the 9 gallon bucket and whatever is left from the 4 gallon bucket is 3 gallons. Transfer the 3 gallons from the 4 gallon bucket to the 9 gallon bucket then fill up the 4 gallon bucket and now you have 7 gallons

8- Fill up 4 gallon bucket then dump it to the 9 gallon bucket. Do this twice and that'll get you 8 gallons.

9- Fill up the 9-gallon bucket

10- Fill up the 9 gallon bucket, then pour 4 gallons onto the 4 gallon bucket twice and what ever is left over has to be 1 gallon because you started with 9 gallons. Then fill up the 9 gallon bucket again leaving you with 10 gallons

11- Fill up the 9 gallon bucket, then pour 4 gallons onto the 4 gallon bucket twice and what ever is left over has to be 1 gallon because you started with 9 gallons pour the 1 gallon onto the 4 gallon bucket. Then fill up the 9 gallon bucket again leaving you with 10 gallons. Then Fill whatever is left from the 4 gallon bucket leaving only 6 gallons on the 9 gallon bucket. Then fill up the 4 gallon bucket by pouring some out of the 9 gallon bucket then dump the 4 gallon bucket leaving you with 2 gallons. Move the 2 gallons from the 9 gallon bucket to the 4 gallon bucket then fill up the 9 gallon bucket. Now you have 11 gallons.

12- Fill up the 4 gallon bucket and dump in the 9 gallon bucket; do this twice. Then fill up the 4 gallon bucket and you have 12 gallons.

13- Fill up both buckets