# Model file for the Google sum problem using a set for the letters

set L := {"W","D","O","T","G","L","E","C","M"};

# var x{i in 1..9, j in 0..9} binary;
var x{i in L, j in 0..9} binary; 

# So, x['D',3]=1 means second letter (D) is equal to digit '3'

minimize objective: 0;

subject to Subtraction
: 
 100000*sum{j in 0..9}(x["W",j]*j) #w
+ 10000*sum{j in 0..9}(x["W",j]*j) #w
+  1000*sum{j in 0..9}(x["W",j]*j) #w
+   100*sum{j in 0..9}(x["D",j]*j) #d
+    10*sum{j in 0..9}(x["O",j]*j) #o
+       sum{j in 0..9}(x["T",j]*j) #t

-100000*sum{j in 0..9}(x["G",j]*j) #g
- 10000*sum{j in 0..9}(x["O",j]*j) #o
-  1000*sum{j in 0..9}(x["O",j]*j) #o
-   100*sum{j in 0..9}(x["G",j]*j) #g
-    10*sum{j in 0..9}(x["L",j]*j) #l
-     1*sum{j in 0..9}(x["E",j]*j) #e
=
 100000*sum{j in 0..9}(x["D",j]*j) #d
+ 10000*sum{j in 0..9}(x["O",j]*j) #o
+  1000*sum{j in 0..9}(x["T",j]*j) #t
+   100*sum{j in 0..9}(x["C",j]*j) #c
+    10*sum{j in 0..9}(x["O",j]*j) #o
+     1*sum{j in 0..9}(x["M",j]*j) #m
;

subject to assign1{i in L}: sum{j in 0..9} x[i,j]=1;
subject to assign2{j in 0..9}: sum{i in L} x[i,j]<=1;