Find the fake coin
One of these coins is a fake. It looks the same but it is a little lighter. Tap coins to put them on the pans, then press Weigh. The lighter pan goes up. When you are sure, press I know the fake and tap it. Use as few weighings as you can.
Left pan
Right pan
Table
What's going on
A balance can do three things, not two. The left pan can go up, the right pan can go up, or they can stay level. So one weighing can sort the coins into three piles: the left pan, the right pan, and the coins you left on the table.
With 9 coins, put 3 on each pan and leave 3 on the table. If a pan goes up, the fake is one of its 3. If they stay level, the fake is one of the 3 on the table. Either way you are down to 3 coins. Now weigh one of those against another and leave the third on the table. Two weighings, every time.
Splitting into two piles feels natural, but it wastes the table. Weigh 4 against 4 and you may be left with 4 coins, and then you need two more weighings.
This demo is a little sneaky. It does not choose the fake until it has to, and it always keeps the fake in the biggest pile it still can. So luck never helps. Only a plan that works every time will do.
Each weighing cuts the pile to a third: 3 coins need 1 weighing, 9 need 2, 27 need 3. How many coins could you handle with 4?
Sheet: Find the fake coin. A cousin of this puzzle, where each question cuts the pile in half: the guessing game.