new puzzle challenge

[Claudio L.]

(03-31-2015 10:03 PM)Claudio L. Wrote:  

(03-31-2015 06:00 PM)Gilles Wrote:  16 linearly equations because of :
A+B+C+D+E+F+G+H+I+J+K+L+M+N+O+P+Q+R+S=190

This is genius! Adding this equation into the mix, we have only 6 independent variables to take care of. This reduces the brute force effort by a factor of 13.
That's only 7 days running non-stop. Big improvement.

Wait... not so fast.
Adding all 15 equations, you get each letter 3 times exactly, so:
3*(A+B+....+R+S)=38*15
3*(A+B+....+R+S)=38*3*5
(A+B+....+R+S)=38*5=190
So that extra equation is not linearly independent.
We still have 7 variables. Back to the drawing board.