Then a year passed

Alright, that was a good year of not blogging, but I'm back, for today, who knows for how long. Anyway, time to post the solution to the funny Knights and Knaves puzzle from last time.

First, I will refer to each person at the party by naming them with the number of truth tellers they claim to have shaken hands with. Now, you can determine right away that person 99 must be a liar, as if he did shake hands with 99 truth tellers then everybody would be a truth teller, including the individual who claims to have shaken hands with nobody. This is a contradiction, so person 99 is a liar. One can continue this down by looking at person 98 next. Since 99 is a liar, in order for 98 to be telling they truth, everybody else must be a truth teller, but this agian would make person 0 a liar, since 98 shook hands with everybody (except possibly 99) in this assumption. So 98 is also a liar.

This logic continues down, making all individuals who claim to have shaken hands with a positive number of truth tellers liars. This leaves only person 0 as a possible truth teller. As there were no other truth tellers at the party, it is certian that person 0 shook hands with no truth tellers, thus person 0 is in fact a truth teller. This gives the answer to the puzzle as 1, there is only 1 truth teller at the party.

Somebody had pointed out to me that there is a silly solution that works out, since the answer is independent of the knowledge of who shook hands with who, it is possible there were no handshakes. In that case person 0 is telling the truth, and everybody else is a liar. This has no contradictions and must be a possible solution, so if there is actually a solution to the puzzle, then the solution must be 1. I'm always reluctant to actually use this sort of solution, as it feels like something of a hack to assume a solution exists and then go from there, but it does often work to use this trick.