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 Near Magic Square Alphametics III (Posted on 2010-03-02)
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.

 No Solution Yet Submitted by K Sengupta No Rating

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 solution | Comment 2 of 3 |

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

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