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1. Using just a 5-gallon bucket and a 3-gallon bucket, can you put four gallons of water in the 5-gallon bucket? (Assume that you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

Yes. Fill the five gallon bucket full. Pour from there into the three gallon bucket, until full. This leaves two gallons in the 5G bucket. Empty the 3G bucket. Now pour the 2 gallons from the 5G bucket into the 3G bucket. Fill the five gallon bucket to the top. Start pouring from the 5G bucket to the 3G bucket. Stop when the 3G bucket is full (remember it already had two gallons in it). This leaves 4 gallons of water in the five gallon bucket.

Done.

JW