[Guest]

In the following 4x4 grid, each of the capital letters 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 represents the number 10*E + T.

[Guest]

There are 4 possible solutions. 2 of them are fro ET = 16 and two of them for ET = 15

So max value of ET is 16 and min is 15

Solutions below:

ET E A S P T R N M L I

16 1 3 4 5 6 8 7 9 2 0

16 1 3 4 5 6 8 0 2 9 7

15 1 4 2 7 5 8 6 9 3 0

15 1 4 2 7 5 8 0 3 9 6

The procedure was rather long to solve various equations and cancelling the common variables and so on...

The trick is to look at rows with common alphabets and the first step is to note that the value of E can be 1 only.

The format has changed!! In the spoiler it seemed ok but on posting the variables are all mixed up!

Edited July 16, 2009 by DeeGee