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 NL.
S C A N
P O L E
A R E A
R E S T
Note: NL represents the number 10*N + L.
As each letter represents a distinct decimal digit, it is easily determined that NL ranges between 14 and 21.
As S+P+A+R = C+O+R+E = A+L+E+S = N+E+A+T
= S+C+A+N = P+O+L+E = A+R+E+A = R+E+S+T,
the following relationships, among others, can be algebraically determined:
A+P = C+S = E+T 2*A = C+O = S+T
A+R = L+S = N+T E+L = P+R = N+C
A+C = P+T A+E = P+S A+N = R+S A+L = R+T
2*P = C+E C+R = L+P E+R = N+P 2*R = L+N
Using these relationships, one can deduce the solution without the aid of a computer:
0 1 2 3 4 5 6 7 8 9 SUM
L R N O T A S C P E 20
Posted by Dej Mar
on 2010-03-02 18:57:26