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Let i represent the index (num in your example) and
...
subject to: sum {over all j} X[i,j] = 1 for all i.
subject to: x[i,j] element of (0,1) for all i, j.

1. For each index/word pair store the number of repeats of each charac
+ter.
2. INIT: Start with the index/word pair that has the highest value by 
+itself (i.e. assuming the value of other index/words are zero). 
...
7. You can repeat this exercise for certain number of iterations and t
+hen you stop with the best solution found thus far. 
NOTE that you can also use randomized approach to randomly pick an ele
+ment to exchange and try to improve the solution.