Stars, hexagons and diamonds this time. Two scales are level, one is not. Work out the missing weight before you peek.
The puzzle
All stars weigh the same, all hexagons weigh the same, and all diamonds weigh the same. Scales A and B are perfectly level:
- Scale A: 1 star and 1 diamond balance 1 hexagon and 2 diamonds.
- Scale B: 2 hexagons balance 1 star and 2 diamonds.
- Scale C: 1 star and 1 hexagon sit on the left pan. The right pan is empty.
How many diamonds must go on the right pan of scale C to make it balance?
Show answer
Answer: 7 diamonds.
- Scale A: take one diamond off each pan. One star now balances 1 hexagon and 1 diamond.
- Scale B: swap the star for 1 hexagon and 1 diamond. Now 2 hexagons balance 1 hexagon and 3 diamonds. Take a hexagon off each pan, and a hexagon weighs the same as 3 diamonds.
- Back to scale A: a star is a hexagon plus a diamond, so a star weighs 4 diamonds.
- Scale C: a star plus a hexagon is 4 + 3 = 7 diamonds.
Check it with numbers: if a diamond weighs 1, a hexagon weighs 3 and a star weighs 4. Scale A is 4 + 1 = 5 against 3 + 2 = 5, scale B is 3 + 3 = 6 against 4 + 2 = 6, and scale C needs 4 + 3 = 7. Any weights that balance A and B are just these scaled up or down, so the answer is always 7.