. How can you find the heavier key with only two measurements on the balances?
A dastardly wizard has locked you in a room with no way of escape. You are presented with 8 keys, all of which appear identical. Seven of the keys are exactly the same weight, and one key is marginally heavier. Only the heavier key will unlock the door, andany of the others will permanently lock it. You cannot discern any difference in weight by holding or examining the keys. You are allowed to use the Wizard’s set of balances to identify the heavier key; but the catch is, he will only let you use it twice. If you succeed in finding the heavier key you are free to go. If not, you will remain as the Wizard’s captive servant.