# Math

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A man selling fruit has only three weights. But with them he can weigh any whole number of kilograms (from 1 kg to 13 kg) inclusive on his balance.

What weights does he have?

Responses

math - Kalyan, Friday, September 5, 2008 at 4:38am
The man had 1kg, 3kg and 9 kg weights.

How do you set it up to get this answer? Any ideas?

• Math -

You can prove to yourself that 1,3 and 9 work. With them, you can form counterbalances of
1, 2 (3-1), 3, 4 (3+1), 5 (9-1-3),6 (9-3), 7 (9+1-3), 8 (9-1), 10 (9+1), 11 (9+3-1), 12 (9+3) and 13 (9+3+1)

A minus sign means putting the weight on the same side of the balance as the weighed object.

Proving that other combinations will not work is harder, but is not necessary.

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