In this 4x4 grid, each of the capital letters in bold represents a different base ten 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 ET.

E   L   M   S
R   E   I   N
A   N  T   I
S   T   E   P

Determine the respective minimum value and the maximum value of ET.

Note: ET is equal to 10*E+ T.

I have discovered two additional solutions, with a value of 14, which should be the correct minimum:

1670   1760

8123   8132

5342   5243

0419  0419

A  E   I   L   M   N  P   R   S   T

5  1   2  6    7   3  9   8   0   4  

5  1  3   7   6   2   9   8   0   4

I was assuming (as in similar alphametics) that a word was a 4-digit number, hence could not begin with zero -- BUT that is not specified here (though ET treated as e*10+ T might suggest this).  Hence minimum is 14 and maximum is 16, with the last four as posted earlier.

Posted by ed bottemiller on 2009-07-31 16:49:39