Your goal is to clear the blocks from the board and lose the least amount of points. That latter part is the most important one, and it is that goal that makes Perfectionist such a unique puzzle — it's an optimization puzzle.

There are 5 rules to the game.

Rule 1. Matching

Combine blocks of same value by first clicking on one, then on the other.

This removes blocks with no loss of points.

Rule 2. Subtracting

Combine blocks of different values. This will subtract the blocks.

When blocks are subtracted, you lose points. In this case a loss of 3 points occurs.

Rule 3. Logistics

You combine blocks by first clicking on one, then on the other. You can only combine blocks horizontally or vertically.

You can go across empty spaces, but you are not allowed to jump over other blocks.

In this example, the 5 can interact with its surrounding blocks 12 7 and 2 but also with block 6

Rule 4. A special block

A block with the value of 1 can be combined with any block on the board.

Rule 5. Endgame

When ten blocks or less remain, the game enters endgame phase. At this point the blocks turn purple and any block can be paired with any other freely.

Most boards will have a minimum score set. This score is not generated but is instead set by players like yourself. If you see that the board is scored, it means that someone has played it before.

The score is not guaranteed to be optimal. If you improve it, your result will replace it.

Keep in mind that solutions are only displayed for past boards. For example, if you want to see how the daily board has been solved, you would need to wait for it to become yesterday's. The switch happens according to the game server's timezone, which is EDT (New York) and is displayed on top.

Once the board is generated, it will now always be accessible. The list of all boards that have ever been generated can be found here.

This means that you can continue working on the board for as long as you like. In fact, some players delibertely seek out boards that haven't been played by anyone or boards with scores which can probably be improved.

The first and most important tip is that you should play a Perfectionist board several times. There is simply no way to get a decent result by going through it only once and, in many ways, playing it just once is missing the point of the puzzle.

The whole beauty of Perfectionist comes through when on your second or third attempt you begin to uncover patterns that you didn't notice in the beginning. A situation which seemed impossible suddenly begins to unfold! It is this effect of unfolding through several attempts at a board that keeps players coming back to the game again and again.

Experienced players consider the first playthrough as getting to know the board, assessing its difficulty and its main challenges.

Weekly boards are awesome!

Although weekly boards might appear to be more intimidating and many players avoid them, in reality they are generally more pleasant to play. You have more options to work with, and there is a rhythm to the game that is less prevalent in the daily boards. You will also have more time to stay with the board and solve it at your own pace.

Fun fact: a weekly board is actually the intended experience. When Perfectionist was first released, for a while it was the only type of board provided.

Deal with the large numbers first

Even if you can't clear them immediately, base your play on preparing the ground to do so with the least loss of points possible. Look for matching numbers in the same row/column and figure out how to clear the space between them efficiently. Use the "Large numbers" mode for better visibility. Play around with the range. By default, numbers 11-15 are considered "large" but sometimes it makes sense to include 9s and 10s too, especially if there are many of them on the board.

The power of 1

1s are very valuable, so use them only when they're really needed. If you need more, consider cheap options to create them by matching low numbers, like 2 and 3, 3 and 4.

Of course, what's cheap can be contextual. Sometimes making a 1 out of 9 and 10 can be a lifesaver.

1s can be used to cheaply remove 2s, especially if a 2 is in the way of larger numbers or if you need to induce an endgame.

Endgame

The endgame phase is crucial. Sometimes you clear the board easily but leave yourself with a difficult endgame situation which then loses you many points.

Consider which numbers are likely to stay till the endgame phase and ensure you have a plan to deal with them.

Groups

Understanding groups is essential to becoming a strong Perfectionist player. This is a bit more advanced and new players don't have to get into this immediately but the sooner you learn to analyze the board through groups, the better.

Perfectionist is a pairing game. Therefore, its all about figuring out how to pair blocks while losing the least amount of points possible.

You normally start with the highest number and see if it appears an even or odd amount on the board. If the amount is even, then in principle this number can be fully paired. Say, there are two 15s. Potentially, you can then pair them without having to involve any other numbers.

If, however, there is an odd amount of them, say, there are three 15s, then you cannot pair them without involving lower numbers. So, the group extends.

The next highest number is 14. We then see if the amount of 15s + 14s is odd or even. If it's odd, the group extends. Let's say there are two 14s. 3(15) + 2(14) = 5, this is odd, so the group extends.

The next highest number is 13. Let's say there is only one. 3(15) + 2(14) + 1(13) = 6. This is even. Therefore, our group is complete and is 15-13.

You then use the same algorithm to identify all the other groups on the board. The "Unpaired Numbers" panel does this analysis for you.

The reason why identifying groups is important is because each time you pair blocks from different groups, the two groups become one. This increases the potential cost.

Say, we have groups 15-13 and 12-7. The minimum cost of pairing 15-13 is 2, the minimum cost of pairing 12-7 is 5.

If you pair 13 and 12 by using a 1, 12 and 13 now appear an even amount each, thus extending the group to 15-7. The minimum cost of this group is 8, plus the 1 that we used to pair 12 and 13.

So, we went from a minimum cost of 7 to a minimum cost of 9.

Things you need to know

Solutions are only displayed for past boards. If you want to see how the daily board has been solved, you would need to wait for it to become yesterday's. Same for the weekly.

When loading the board using a seed, make sure you choose the type first (daily or weekly). If your type is wrong, the board will still be generated but your result will not get saved to the server.

The server will only accept results from boards that have been officially generated. You can create a board using the "Enter seed" option but if its seed and type don't match any of the boards previously generated, your result will not be saved.

Random boards

The "Random" option will select an official board at random. You can safely play these, in the sense that your result will be saved.

You might notice that quite a number of boards have a score set but have no rankings. This is due to the fact that the rankings feature was introduced much later, whereas the ability to store and display the best score was there from the start. If you manage to beat the score on one of those boards, your ranking will then be displayed!

Since there are more daily boards than weekly ones, you're more likely to get a daily board. If you want to play more weekly boards, you can simply choose one from this list by copying its seed. Make sure to pick the right type first (the button on top should say "type:weekly"), then click "Enter seed" and paste the board's seed.

In the perfect world the optimal score would simply be generated and serve as a target that the player should try to reach. Unfortunately, there is no known algorithm to solve a Perfectionist board. In computer science parlance, Perfectionist is a problem that's NP-complete, which means that its solution is trivial to verify but not trivial to implement. Specifically, Perfectionist seems to be somewhat related to the Subset sum problem.

What this essentially means is that when you see a board which no one has played, there's no way to tell beforehand what it's optimal score might be. For some boards going below 20 would be trivial, for others even getting below 30 might prove impossible. So, you have to treat each board individually. The goal of the game is to try to get as close as possible to the optimal score for that particular arrangement.

Because getting a good score is not easy, there is no need to create a complicated authentication system in order to allow people to submit scores. The server will not add your score unless it's a valid playthrough and unless the resulting score is better than the one set by the previous player. Therefore, your solution is a kind of mathematical authentication, and you can't do better than the mathematical limit of any given board.

Another interesting implication of how Perfectionist works is that there are almost no universally easy or hard boards. A board might feel easier or more pleasant to play because matching the blocks might require less tradeoffs. However, often a more skilled player might be capable of optimizing the common solution and shaving off several points. Sometimes finding a way to reduce the score you're getting by just one point could be a tricky exercise.

The boards are completely random and are generated using a seeded Mersenne Twister pseudorandom number generator. This makes each board reproducible on demand.

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.