Is this an original puzzle?
Yes. It was invented by Louigi Verona in 2016.
How are the boards generated?
The boards are completely random and are generated using a seeded Mersenne Twister pseudorandom number generator. This makes each board reproducible on demand.
Because each board is random, there is no guarantee that it will be perfectly solvable. In fact, the vast majority of boards are not perfectly solvable, and the goal is to find an optimal solution.
In the current implementation of Perfectionist the seed range is between 1 and 2147483647. Obviously, the amount of all boards possible is way larger than that, but for now 2 billion boards should be a good enough pool.
I also considered generating the so-called Null Boards, perfectly solvable boards. However, my experiments have shown that most of these boards are boring to play.
Can an optimal solution be mathematically calculated?
Solving Perfectionist seems to be closely related to the subset sum problem, which is NP-complete. This means that a solution to such a problem is relatively easy to verify but there is no trivial way to find a solution quickly.
Of course, there are probably ways to find a solution using various heuristics or focus on finding a good enough solution, as opposed to the optimal one.
From time to time folks attempt to write solvers, like this one or this one. At some point one of the players hosted a Discord bot that was able to solve boards. If you're interested in giving it a go, be sure to join our Discord server and share your work!
Why is there only one board per day?
Since Perfectionist looks similar to many casual games, with colored blocks and numbers, the challenge was to get players to see Perfectionist for what it really is - a very satisfying but also a challenging puzzle, the intellectual beauty of which can only be recognized through repeated attempts at a board. In previous incarnations of the game people would tend to try a board, get stuck, reload for a new board, get stuck again and lose interest.
Having Daily and Weekly Boards helps drive home the fact that each puzzle should be played several times, and that this is, in fact, the whole point. It is after the introduction of these periodical boards that I've noticed a sharp increase in the appreciation of the game from new players.
Strictly speaking, the original Perfectionist was designed as a 9x11 board, so in my opinion, Weekly Boards tend to be more satisfying. They offer more options, more planning and a deeper gameplay. Daily Boards, by virtue of being smaller, are a bit more brutal.