Substitute each of the capital letters in this 4x4 grid by a different digit from 0 to 9, such that the sum of each of the four columns as well as the sum of each of the four rows is TO.

S   H   O   P
P   I    P   E
A   R   E   A
R   E   N   T

Note: TO represents the number 10*T + O.

I grossly misread this. 

I derived a solution based upon my original understanding but as there appeared to be more than one possibility I wrote a computer listing which offered a multitude of solutions!

Edited out my original post.

Noting the frequency of letters and computing their maximum and minimum sums:
        A   E   H  I  N  O   P   R  S  T
Freq  2   3   1  1  1  1   3   2   1  1
        7   9   5  4  3  2   8   6   3  1
Max 14 27   5  4  3  2 24 12   3  1  Total=95  Av=23.75

        3   0   4  5  6  7   1   2   8  9
Min   6   0   4  5  6  7   3   4   8  9 Total=52  Av=13

TO must therefore be a value from 13 to 23.

A partial edit of my listing shows TO to be 20.

I'll leave that as a hint for those who might care to manipulate the grid values since I now have a unique solution.

Edited on October 4, 2009, 1:19 am

Posted by brianjn on 2009-10-03 22:21:15