Imagine that you are locked in a room with only these things: some sacks of some gold coins, a penny scale, and one penny.
The exact number of sacks does not matter, and the exact number of coins in each sack does not matter. It just matters that there are plenty of coins in each sack to work with. Imagine around 10 sacks, and around 100 coins in each sack.
One sack contains all fake gold coins. All of the other sacks contain all real gold coins. The fake coins are indistinguishable from the real coins in appearance; however, each real gold coin weighs 1 oz , and each fake coin weighs 1.1 oz.
It costs one penny to weigh something on the scale, so you may only weigh something one time.
How can you find out which sack is the fake?
This puzzle was featured on an episode of a TV show called Columbo (season 6, episode 3) .
Look dude....we don't need any of that c**p on here.......put a sock in it.......
Number the sacks from 1 to 10.
Take 1 coin from sack No.1, 2 coins from sack No.2, 3 coins from sack No.3.............to 10 coins from sack No.10. Add them all up: 1+2+3+4..........+10 =55. Anything over 55 such as 55.7 ounces, that simply means that sack No.7 is the fake one, since 7 coins are overweight by: 7 x 0.1 ounces =0.7 of an ounce.