My dear friend @ajk44 pointed me at a puzzle on the excellent Nrich site1, and I enjoyed it enough to share my solution. (If you don’t want it spoiled, don’t read beyond the blockquote.)
Four jewellers had respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds.
Each gave one gem from their collection to each of the rest.
Afterwards they noticed that they all had collections of gems of precisely equal value.
Can you work out the relative values of each gem?
Can you then work out how much each jeweller gained or lost?
A first approach
The first thing I tried was to set…
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