/sci/ - Science & Math

>>15169247
Nice job! That is indeed the correct answer.
>Thanks for the entertainment
Thank you a lot more for taking the time to solve it. I'm grateful.
>Now, what is the solution to the general problem?
What a great question.
I apologize but I may not be able to give you a satisfactory answer when it comes to this.
Well, if you mean general as in how many at most two-to-one functions there are from [n] to [n], then I believe it may look something like pic related. My friend found it and I also found something similar. To be clear, I'm not 100% certain this is true but I don't see why it would be wrong.
If you google A012244 you'll find the OEIS page for this sequence. Perhaps that will interest you.
However for i-to-one functions in general, I'm afraid I don't have an answer. Another friend of mine mentioned that they had found it, however they have not shared it yet.

If you do find something that you think is interesting, I'd appreciate you sharing it here. I shared this problem without actually knowing how nice it was but as usual it seems to be more fun than it first seemed. When and if my friend shares the general answer, I'll let you know and put it here hopefully. And in the meantime you could check pic related and see if you think it's correct. Again, I and my friend do but that does not guarantee it. Have a nice day, hope we talk again soon.

oh and also we have a discord if you're interested for problems like this, it's bit dead but meh, let me know if you'd like to join.