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Puzzle image: made for aglena.
Apples, pears and cherries are sitting on three old-fashioned balance scales. The first two are perfectly level. Every apple weighs the same, every pear weighs the same, and so does every cherry. Can you work out how many cherries it takes to level the third scale?
The puzzle
- Scale 1: an apple and a cherry balance two pears.
- Scale 2: a pear and a cherry balance one apple.
How many cherries balance two apples and a pear?
Show hint
Scale 2 tells you exactly what an apple is made of. Swap that into scale 1, then take the same fruit off both sides.
Show answer
Answer: 8 cherries.
Puzzle image: made for aglena.
- Scale 2 says an apple weighs the same as a pear plus a cherry.
- Swap that into scale 1: a pear, a cherry and a cherry balance two pears. Take one pear off each side, and a pear weighs 2 cherries.
- Back to scale 2: an apple is a pear plus a cherry, so an apple weighs 3 cherries. Check scale 1: 3 + 1 = 2 + 2.
- Two apples and a pear weigh 3 + 3 + 2 = 8 cherries.
The trick is that you never need to know what a cherry actually weighs. Measuring everything in cherries is enough to level the last scale.
