I was wondering today if I was generally faster on the first timed puzzle of a given size on a given day, and then I remembered that the data to answer that likely exists, so I figured I'd bring it up and see if there was any difference.

So basically, the list of questions I came up with:

1. Is there an overall tendency to have the fastest time of the day come from a specific puzzle based on the order in which the puzzles were presented? i.e. is the average user faster on the 1st puzzle of a given size, the 4th puzzle, or is it completely random.
2. If there is an effect, what happens if there's a delay in the middle of solving the puzzles?
3. Are there individual preferences? i.e. I might be statistically significantly faster on the 1st puzzle, but another user might be faster on the 4th.
4. If there are individual preferences, do they carry over from size to size? i.e. given that someone is faster on the 1st puzzle of 4x4's, what's the probability that they are also faster on the 1st puzzle of 5x5's?

Edit: Oh, and 5, do faster solvers have a different preference set from the broader population?

I should probably collect some anonymized data and publish that,
so people like you can get cracking

It probably depends on how people approach the puzzle. Assuming you are likely to be anyway competitive for top 25 or, in particular, top 10, it probably makes sense to put down a marker early on. This would allow you to take chances/guesses in later attempts without worrying too much about going wrong.

In my case, I usually try to do the first two puzzles quickly (by guessing, where appropriate) and, if I crash and burn, I do the third attempt slowly and methodically in order to ensure I have submitted a time. This then allows me to take a flier on the final attempt.

Mind you, I’m something of a slowcoach (not helped by the fact that I’m using a tablet) and I have never had a top 25 score on the 4x4 and I’d say I get a top 25 on the 5x5 maybe 3 or 4 times a year and on the 6x6 maybe once a month.