Three balance scales, three kinds of shapes, and one empty pan. Give yourself a couple of minutes and see if you can work out the missing weight before you peek.
The puzzle
All squares weigh the same, all triangles weigh the same, and all circles weigh the same. Scales A and B are perfectly level:
- Scale A: 1 square and 1 triangle balance 3 triangles and 1 circle.
- Scale B: 1 triangle and 1 circle balance 3 circles.
- Scale C: 1 square and 1 circle sit on the left pan. The right pan is empty.
How many circles must go on the right pan of scale C to make it balance?
Show hint
If a scale is level, you can lift the same shape off both pans and it stays level. Start with scale B.
Show answer
Answer: 6 circles.
- Scale B: take one circle off each pan. One triangle now balances 2 circles, so a triangle weighs the same as 2 circles.
- Scale A: take one triangle off each pan. One square now balances 2 triangles and 1 circle. Swap each triangle for 2 circles, and the square weighs the same as 5 circles.
- Scale C: a square plus a circle is 5 circles plus 1 circle, so you need 6 circles on the right pan.
Check it with numbers: if a circle weighs 1, a triangle weighs 2 and a square weighs 5. Scale A is 5 + 2 = 7 against 6 + 1 = 7, scale B is 2 + 1 = 3 against 3, and scale C needs 5 + 1 = 6. Any set of weights that balances A and B is just this set scaled up or down, so the answer is always 6.