# ILP Part 73 — Matchstick puzzle

This is the seventieth third part of the ILP series. For your convenience you can find other parts in the table of contents in Part 1 – Boolean algebra

Today we’re going to solve a matchstick puzzle. Move one stick to make the equality hold:

which is 6 + 2 = 9.

Solution is rather trivial but let’s encode it in ILP:

We use 7 segment displays with elements in this order:

so it is top, top-right, bottom-right, bottom, bottom-left, top-left, middle.

In line 1 we specify initial state. In lines 2-3 we define how many moves to make and how many digits in total we have.
Next, in line 6 we define matches, and in line 9 we define variables for digits.

In lines 12-14 we specify that digits must be less than ten. Next, in lines 16-17 we specify that at most one match of the initial state can be moved.

Next, in lines 19-52 we translate 7 segment displays to digits. We define patters in lines 22-33. Next, in liens 35-51 we iterate over patterns, take respective segments, and make sure that if segments are set then digit is formed accordingly.

Finally, in line 54 we define the equation.

Output:

It worked in 0.02 second.