My guesses:

Field and Farmer: Go to the edge where the farmer comes close to you, then run the opposite direction he is facing so he has to go around the entire circle to catch up...

20 prisoners: If they are in the same block, they could count each time they hear the doors to their cells open.

Coins on the table: Flip all the coins...put half on the table and half on the floor...

Random Riddle from the intarwebs...


"A farmer challenges an engineer, a physicist, and a mathematician to fence off the largest amount of area using the least amount of fence.

The engineer made his fence in a circle and said it was the most efficient.

The physicist made a long line and said that the length was infinite. Then he said that fencing half of the Earth was the best.

The mathematician laughed at the others and with his design, beat the others. What did he do?"