So this one day, I am playing the board game Quarto with

my boyfriend.

Quarto is a variant of four in a row, with two twists:

One: The pieces have 4 attributes, instead of just 1 like in normal four in a row,

where pieces just vary in color. In Quarto, pieces vary

in shape, size, color and form of the top, as you can see

here

You win if you get four pieces in a row who all have the

same property.

The other twist is that you pick a piece, which your

opponent then places, but this is irrelevant for this talk.

In university I followed a wonderful course on how to solve puzzles like this, by using boolean satisfiabiliy

How exactly will it help us if we convert the problem to

SAT?

Let’s dive into how an SAT solver works.

No, trying all options would be too slow. SAT solvers have a use a few tricks to reduce

the state space

The input is generated now and converted to CNF. Would

it be satisfiable??

Suspense... Is.... Killing me!

There it is, the assignment and the accompanying board.

Woohoo, we did it!

Next question of course is, how many of such boards

exist?

Thanks for watching, the code is on github!