Speed, accuracy and difficulty all have to be in the same number. Here is the reasoning behind the formula, and the two things we refused to reward.
A score is a claim: it says this run was better than that run. Designing one means deciding what "better" means, which is more of a values question than a maths question.
We made two decisions early that shaped everything else, and both were refusals.
We refused to reward raw speed alone
A pure speed score rewards mashing. It also makes the leaderboard a typing contest on the easy levels, which is not interesting for anyone.
So speed enters as a multiplier on a difficulty-weighted base, and accuracy subtracts from it. A fast wrong run scores less than a slow right one.
We refused to reward time spent
The opposite error is scoring persistence — which turns a five-minute coffee-break puzzle into homework and quietly punishes everyone with a job.
The daily is designed to take three to five minutes. The scoring is built so that a good run in that window beats a grinding one.
Difficulty has to be worth more than convenience
Level three carries the largest multiplier because it is the level that actually discriminates between strong players. If all three levels scored equally, the leaderboard would be decided on level one.
This is also why replaying the easy level cannot raise your ranked score: only your first run per day and level counts.
And we had to decide what to do about cheaters
We cannot stop someone from writing a solver. What we can do is refuse to rank runs we cannot reproduce, and refuse to rank runs where the player left the tab mid-puzzle.
The honest position is that the leaderboard is a game for people who want to play it, not a secure competitive environment. We would rather say that plainly than pretend otherwise.