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'I have a pair of scales and 3 weights and with these 3 weights I can weigh any number of pounds from 1 up to 13.(I may, of course, find it necessary to put one or more weights in both scales.) What are my 3 weights?

I have to say that I was stumped trying to calculate it. The best I could do was to assume that one weight (a) would have to be 1lb and that all 3 weights (a + b+ c) would add up to 13. Therefore b + c = 12. Beyond that I was stuck!

This shows the level thought, back in those days, that was considered OK for children of this age.

Can this be calculated or only solved empirically?