[Guest]

Substitute each of the capital letters in this 5x5 square by a different digit from 0 to 9 such that each of the columns, each of the rows as well as each of the main diagonals has the common sum TKU, where T is nonzero, and numbers in each of the cells contains non leading zero.

TI   KT   NS   OB    UL


CN   IO   CC   UK    TB


IU   OL   UI   SC    CS


OK   UB   TL   KO    IT


NC   TK   KU   NN    OI

Note: Each of the numbers in the cells represent a two digit number. For example, TI represents the number 10*T + I (rather than the product T*I).

Similarly, TKU represents a 3-digit number (rather than the product T*K*U).

Edited August 12, 2009 by K Sengupta

[Guest]

Just convert all of these to algebraic equations:

As in: TI+KT+NS+OB+UL=TKU would mean:

10T+I+10K+T+10N+S+10O+B+10U+L=100T+10K+U

You have 12 equations and only 9 variables, that should be solvable, it'll just take really long...