In this example, the solution to the puzzle is:
\nO = 0, M = 1, Y = 2, E = 5, N = 6, D = 7, R = 8, and S = 9.<\/p>\n
which gives us:<\/p>\n
9567\r\n+ 1085\r\n---------\r\n= 10652\r\n<\/pre>\nAnother example<\/strong> is give below<\/p>\n
CP\r\n+ IS\r\n+ FUN\r\n--------\r\n= TRUE\r\n<\/pre>\nHere, the solution is R=0, T=1, C=2, P=3, S=4, E=5, U-6,<\/span> I=7, N=8, F=9<\/span><\/p>\n
which gives us:<\/p>\n
23\r\n+ 74\r\n+ 968\r\n--------\r\n= 1065<\/pre>\n<\/p>\n
Modelling the Problem<\/strong><\/p>\n
Step 1<\/strong>: The first step is to identify the variables. In this case, out variables are all the letters in the problem. They are:<\/p>\n
C, P, I, S, F, U, N, T, R, E<\/p>\n
Not that there will be not repeating variable. Also, the values of the variable are single digits, therefore the ranges are 0 to 9. The code below defines the variable.<\/p>\n
from<\/span> ortools.sat.python<\/span> import<\/span> cp_model\r\nmodel =<\/span> cp_model.<\/span>CpModel()\r\n<\/pre>\nThe next code sets up the variables
\n<\/p>\nbase =<\/span> 10<\/span>\r\n\r\nc =<\/span> model.<\/span>NewIntVar(1<\/span>, 9<\/span>, 'C'<\/span>)\r\np =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'P'<\/span>)\r\ni =<\/span> model.<\/span>NewIntVar(1<\/span>, 9<\/span>, 'I'<\/span>)\r\ns =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'S'<\/span>)\r\nf =<\/span> model.<\/span>NewIntVar(1<\/span>, 9<\/span>, 'F'<\/span>)\r\nu =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'U'<\/span>)\r\nn =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'N'<\/span>)\r\nt =<\/span> model.<\/span>NewIntVar(1<\/span>, 9<\/span>, 'T'<\/span>)\r\nr =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'R'<\/span>)\r\ne =<\/span> model.<\/span>NewIntVar(0<\/span>, 9<\/span>, 'E'<\/span>)\r\n\r\n# List of variables<\/span>\r\nletters =<\/span> [c, p, i, s, f, u, n, t, r, e]\r\n<\/pre>\n<\/p>\n
Step 2:<\/strong> Then we identify the constraints<\/p>\n
The variables are letter and can take on single digit value<\/p>\n
Therefore we can establish the following constraints<\/p>\n
\n
- CP + IS + FUN = TRUE<\/li>\n
- each of the letter must be a different digit<\/li>\n
- C, I, F, T \u2260 0 (since leading digit in a number is not zero)<\/li>\n<\/ul>\n
The code below defines the constraints and the objective function<\/p>\n
# Define the constraints<\/span>\r\nmodel.<\/span>AddAllDifferent(letters)\r\n\r\n# CP + IS + FUN = TRUE<\/span>\r\nmodel.<\/span>Add(c *<\/span> 10<\/span> +<\/span> p +<\/span> i *<\/span> 10<\/span> +<\/span> s +<\/span> f *<\/span> base**<\/span>2<\/span> +<\/span> u *<\/span> 10<\/span> +<\/span> n ==<\/span> t *<\/span> 10<\/span>**<\/span>3<\/span> +<\/span> r *<\/span> 10<\/span>**<\/span>2<\/span> +<\/span> u *<\/span> 10<\/span> +<\/span> e)\r\n<\/pre>\n<\/p>\n
Step 3:<\/strong> Printing all Solutions<\/p>\n
We want the solver to print\u00a0 the solution as it finds them. The code below does that:<\/p>\n
# Solution Printer Class<\/span>\r\nclass<\/span> VarArraySolutionPrinter<\/span>(cp_model.<\/span>CpSolverSolutionCallback):\r\n \r\n def<\/span> __init__<\/span>(self<\/span>, variables):\r\n cp_model.<\/span>CpSolverSolutionCallback.<\/span>__init__(self<\/span>)\r\n self<\/span>.<\/span>__variables =<\/span> variables\r\n self<\/span>.<\/span>__solution_count =<\/span> 0<\/span>\r\n \r\n def<\/span> on_solution_callback<\/span>(self<\/span>):\r\n self<\/span>.<\/span>__solution_count +=<\/span> 1<\/span>\r\n for<\/span> v in<\/span> self<\/span>.<\/span>__variables:\r\n print<\/span>('%s=%i '<\/span> %<\/span>(v, self<\/span>.<\/span>Value(v)), end=<\/span>''<\/span>)\r\n print<\/span>()\r\n \r\n def<\/span> solution_count<\/span>(self<\/span>):\r\n return<\/span> self<\/span>.<\/span>__solution_count\r\n<\/pre>\n<\/p>\n
![\"Solution](\"https:\/\/www.kindsonthegenius.com\/data-science\/wp-content\/uploads\/sites\/12\/2021\/01\/Screenshot-2021-01-21-at-22.48.53.png\")
<\/a>