Here is another “thinking inside the box” puzzle, this one from Jeff Rush through Elliot.
You have 12 golf balls. 11 are identical. The 12th is outwardly identical but weighs a slightly different amount. Your task is to identify the different ball and specify whether it is too light or too heavy. You have at your disposal only a simple two-pan balance scale on which you can place one or more balls to compare their weights. You may use the scale only three times. What three measurements will you do that will guarantee that you can correctly identify the different ball?
The solution took me an hour to discover and does not involve any tricks. No additional objects, tricky ways to use the scale, etc. Just put two sets of balls on the scale and see what happens. Repeat twice with different sets of balls, and announce the answer. The problem is all in which balls to test in which order.
As with the other puzzle, it at first seems to be impossible, but attempting to prove it impossible led me to the answer.