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Puzzle image: made for aglena.
Rubies, emeralds and diamonds are sitting on three old-fashioned balance scales. The first two are perfectly level. Every ruby weighs the same, every emerald weighs the same, and so does every diamond. Can you work out how many emeralds it takes to level the third scale?
The puzzle
- Scale 1: two rubies and an emerald balance one diamond.
- Scale 2: a diamond and an emerald balance three rubies.
How many emeralds balance a diamond and a ruby?
Show hint
Swap the diamond from scale 1 into scale 2, then cancel matching gems on both sides until only rubies and emeralds are left.
Show answer
Answer: 7 emeralds.
Puzzle image: made for aglena.
- Scale 1 says a diamond weighs the same as two rubies plus an emerald.
- Swap that into scale 2: two rubies, an emerald and another emerald balance three rubies. Take two rubies off each side, and a ruby weighs 2 emeralds.
- Back to scale 1: a diamond is two rubies plus an emerald, so a diamond weighs 5 emeralds. Check scale 2: 5 + 1 = 2 + 2 + 2.
- A diamond and a ruby weigh 5 + 2 = 7 emeralds.
The trick is that you never need to know what an emerald actually weighs. Measuring everything in emeralds is enough to level the last scale.
