"engsol" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > There is a number puzzle which appears in the daily paper. > Because I'm between Python projects, I thought it might be > fun to write a program to solve it....20 minute job, max. > > On closer inspection, it became apparent that it's not a > simple thing to program. How would you approach it? > > The puzzle: a 4 x 4 grid. The rows are summed (and given), the > cols are summed (and given), and the two diagonals are summed, > and given. In addition, 4 clues are given, but none of the 4 are in > the same row or col. > > Example from today's paper:...solution time is 8 minutes, 1 second, > so they say. > > The set of allowable numbers is 1 thru 9 > > Rows: > 3 + B + C + D = 22 > E + F + 8 + H = 26 > I + J + K + 8 = 31 > M + 7 + O + P = 25 > > Col sums: > 24, 18, 31, 31 > > Diag sums: > 3 + F + K + P = 24 > M + J + 8 + D = 24 > > > > The first impulse is to just brute force it with nested for loops, > but the calculator shows the possible combinations are > 9^12 = 5,159,780,352, which would take much too long. >
What you have is a set of 10 linear equations in 11 variables. Normally that isn't enough to generate a unique solution, but the additional constraint that all variables must have values in the range 1..9 probably will get you to a unique solution. I suggest you Google for techniques for solving "simultaneous linear equations". -- I don't actually read my hotmail account, but you can replace hotmail with excite if you really want to reach me. -- http://mail.python.org/mailman/listinfo/python-list
