Omer S.

asked • 06/07/15# prove that for every 8 choosen numbers from 10 to 36 you can always make equalities.

number can be used once. examples. let say that the choosen numbers are 10, 11, 12, 15, 18, 25, 32, 36 you can write 11+25=36 or 10+12+18=15+25. i tried to prove for summation for every 2 numbers $$\binom{8}{2}=28 $$ but there are 51 different summation that's the closest i got

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## 1 Expert Answer

Mark M. answered • 06/07/15

Mathematics Teacher - NCLB Highly Qualified

You ask for a proof for "every" 8 chosen numbers.

I choose 10, 11, 12, 13, 14, 15, 16, 17.

None of these numbers can be expressed as the sum of some of the other 7.

The contrary example negates the conclusion.

The first number than does satisfy is 21.

Omer S.

thanks for the help, but you are not the one who choose, for any choosen number

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06/08/15

Omer S.

is't for every choosen number

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06/08/15

Mark M.

tutor

The problem states prove "for

**every**8 numbers. The phrase "for every" means "for any." If a counter example can be presented, which I have done, the proof is not possible no matter who gets to choose.
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06/08/15

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Mark M.

06/07/15