Kakuro questions by email

This question came by email:

I am a physics student and I have the following question regarding the Kakuro problem: do we have to implement the 11 constraints as they are or can we tweak them a little bit? Specifically, for instance, we have the following constraints that must be implemented “x0 != x1” and “x0 != x2”. But x0, x1 and x2 are 1 qubit registers. So if these conditions are true, that means that when x0 = 0, then x1 = 1 and x2 =1, so we could rewrite these conditions as "x0 != x1 and “x1 = x2” which reduces the number of registers needed and obviously Cx gates (I can just use 1 qubit to represent both x1 and x2 because they have to be the same for any solution). Is this valid? Or are we obligated to implement the constraints as presented (it feels a bit silly to implement these 2 constraints separately because it is essentially the same thing twice, but with different qubits).

The answer is: you have the implement the 11 constraints that we defined without simplifying them farther