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?
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.