About Balance Scale
Fake coin puzzles ask you to find one counterfeit among coins that look the same, using only a balance scale. Each weighing has three possible results: the left pan goes down, the right pan goes down or the scale balances. That is why three coins need one weighing, nine need two and twenty-seven need three, as long as you know the fake is heavier. When it could be heavier or lighter the puzzle gets much harder, and the twelve coin version, which spread widely in the 1940s, is one of the best known logic puzzles of all.
How to play Balance Scale
- One coin is a fake that weighs a little more (or, in some puzzles, more or less). Tap a coin to put it on the left pan, again for the right pan, again to take it off.
- Put the same number of coins on each pan and press Weigh: the heavier side goes down, or the scale balances.
- When the weighings prove which coin is fake, press Answer, tap the coin and, if asked, say heavier or lighter. Notes let you mark coins as you go.
- The scale never picks the fake in advance, so luck can’t help: plan each weighing. The fewest weighings earn three stars, and your progress is saved on this device only.
Tips & strategy
- Split the coins into three groups, not two: two on the scale and one off it. Each weighing tells you which group holds the fake.
- When the fake could be heavier or lighter, a coin that has been on the down side once and the up side once must be good. Keep notes.
- Coins already proven good are useful: put them on the scale to make the groups the sizes you need.
- Before you weigh, plan for all three results. If one would leave too many coins, change the weighing.
Balance Scale: questions and answers
How many weighings do I need?
With a heavier fake, one weighing settles up to 3 coins, two up to 9 and three up to 27. When the fake could be heavier or lighter and you must say which, three weighings settle up to 12 coins, or 13 with a spare coin known to be good.
Why can’t I get lucky?
The fake is not chosen at the start. After each weighing the scale gives the result that leaves you the most to do, while always staying true to some coin. So an answer only counts when the weighings prove it.
Do wrong answers count?
Yes: each wrong answer counts as one more weighing towards your stars, but it never ends the puzzle.