Of the 26 numbers 144, 145, 146, ..., 168, 169, twenty-fi ve of them are arranged into a 5 by 5 array so that the sums of all rows and the sums of all columns are the same. Which could be the number that was omitted?

Guest May 9, 2020

#1**0 **

There are patterns that can be used to make a 5 x 5 magic square (not only are the sums of all the rows and all the columns the same, but also the sums of the two diagonals).

Using one of these patterns, I constructed a magic square that used the first 25 numbers, omitting 169.

Then, using the same pattern, I constructed a magic square that used the last 25 numbers, omitting 144.

So, there are at least two answers to your question: either 169 or 144.

geno3141 May 9, 2020