3. Sally had 5 and Anna had 3.

70

1 cent.

His son.

The accounting method is wrong. The $2 is actually a part of the $27, and shouldn’t be added to it as stated in the problem.

You ask either man the following question: “If I asked the other guy which door has the money, what would he say?”, then choose the opposite door. Work it out: If you ask the question to the liar, he will lie about the ‘correct’ answer, so you must choose the opposite door. If you ask the truth teller, he will tell the truth about the lie, so you can choose the opposite door as well.

Fill the 5 gallon jug, pour it into the 3 gallon jug until the 3 gallon is full, leaving 2 gallons in the 5 gallon jug. Now pour the 3 gallon jug out. Pour the remaining 2 gallons from the 5 gallon into the empty 3 gallon jug. Now fill the 5 gallon from the faucet. You now have exactly 7 gallons.

Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.

This is possible, and there are 2 ways to do it: Solution 1: Fill the 3 cup bucket, pour it into the 5 cup bucket. Fill the 3 cup bucket again, and pour it into the 5 cup bucket until the 5 cup bucket is full. That will leave exactly 1 cup of sugar in the 3 cup bucket. Dump out the 5 cup bucket, and dump the 1 cup from the 3 cup bucket into the empty 5 cup bucket. This leaves 1 cup in the 5 cup bucket. Now fill the 3 cup again and add it to the 5 cup bucket. Now you have exactly 4 cups of sugar in the 5 cup bucket! Solution 2: Fill the 5 cup bucket. Pour it into the 3 cup bucket. This leaves 2 cups in the 5 cup bucket. Dump out the 3 cup bucket. Now pour the 2 cups from the 5 cup into the 3 cup. Refill the 5 cup. Now pour the 5 cup into the 3 cup until the 3 cup is full. That will leave exactly 4 cups in the 5 cup bucket!

Three. In the worst case, the first two socks you take out will consist of one black sock and one white sock. The next sock you take out is guaranteed to match one or the other.