# Thread: [SOLVED] is this possible???

1. ## [SOLVED] is this possible???

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?

2. Originally Posted by shosho
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?

No. If it were possible and each column sum were x, the the sum of the
number from 1 to 240 would be 16x, so this sum would be divisible by 16.
But the sum of the integers from 1 to 240 is 120*241=28920, which is
not divisible by 16.

RonL

3. hey thanx

but im not sure how you got the sum? could you please explain your solution again?
thanx

4. Originally Posted by shosho
hey thanx

but im not sure how you got the sum? could you please explain your solution again?
thanx
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