Question

Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.

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Miles

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sum of natural numbers from 1 to 240
=\frac{240\times241}{2}=28920
number of columns = 16
for equality, each slumn should have the sum as 28920/16 = 1807.5 which is a fractional number
we are only putting integers, and hence sum of each column has to be an integer and Not a fraction.
Hence the given statement is proved

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