# Divide $40$ to $4$ parts such that every number from $1-40$ can be realized

How can you divide $40$ to $4$ parts such that every number from $1-40$ can be realized just by adding or subtracting those $4$ parts?

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See the balanced ternary number system. –  Marc van Leeuwen Dec 13 '12 at 12:41

All integers from 1 to 40 can be expressed by adding or subtracting 1,3,9 and 27 in such a way that each number is used at most once, and it should be either added or subtracted.

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You mean, "each number is used at most once". –  TonyK Dec 13 '12 at 13:25
Oops. That's true. –  Host-website-on-iPage Dec 29 '12 at 7:04