Is it possible to arrange the integers from 1 to 240 in a table with 15 rows and 16 columns so that the sum of the numbers in each of the columns would be the same?

thanx in advance for your help =)

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- Aug 8th 2007, 10:40 PM #1shoshoGuest

- Aug 8th 2007, 10:47 PM #2

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- Aug 10th 2007, 05:01 PM #3shoshoGuest

- Aug 10th 2007, 11:39 PM #4

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Let the sum of each column be x, then the total sum is equal to the sum of

the column sums (that is you add down the coulmns then accross the column

sums. But this is equal to the sum of the integers from 1 to 240, you are

supposed to know that the sum of the first n positive integers is

s=n(n+1)/2,

So in this case n=240, and s=120 241.

This should be equal to 15x, but as s is not divisible by 15 no such x exists as

an integer, so the task is impossible.

RonL