# Find the lighter coin: visual puzzle and solution | SwaVid

Nine identical coins include one lighter coin. Can you identify it with exactly two balance-scale weighings? See the complete step-by-step solution.

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Source: https://www.swavid.com/puzzles/nine-coins

# Find the lighter coin

## Yes: weigh 3 vs 3, then 1 vs 1.

### Split into three groups of three

### Read the first weighing

### Weigh one against one

SwaVid visual puzzle

Nine identical coins include one lighter coin. Can you identify it with exactly two balance-scale weighings?

Detailed solution

A balance has three outcomes (left, right, balanced), so one weighing can split the coins into three groups, not two.

Put three coins on each pan and leave three aside.

If a pan rises, the light coin is in that pan's three. If the pans balance, it is in the three you set aside.

From the suspect three, weigh two coins. The one that rises is lighter; if they balance, the third coin is the light one.

Splitting 4 vs 4 uses only two of the three outcomes, so two weighings can only sort 4 coins, not 9.

- 1 Split into three groups of three Put three coins on each pan and leave three aside. 9 = 3 + 3 + 3
- 2 Read the first weighing If a pan rises, the light coin is in that pan's three. If the pans balance, it is in the three you set aside. 3 outcomes → 3 groups
- 3 Weigh one against one From the suspect three, weigh two coins. The one that rises is lighter; if they balance, the third coin is the light one. 3 outcomes → 3 coins

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