Puzzle thread? Puzzle thread.

[Xei]

Congrats to Nelzi and Dub for getting the farmer one, and to Nelzi for getting the coin one! Their answers basically boil down to this: Spoiler for Solution to the field and the farmer: The basic trick is to realise that if you run around a small circle centred on the centre of the field, you can outpace the farmer. In fact, if the circle is a quarter of the distance from the edge, the circumference will be 4 times less, and you and the farmer will take the same time to do a lap - so on a circle a tiny bit smaller than this one, you can outpace the farmer. So run around this circle until you're on the opposite side of the centre to him. Then just run in a straight line to where the path is closest. The farmer has to travel half of the way around the circular field to meet you there, and it's easy to check that this is more than 4 times as far. So you can always make it. Spoiler for Solution to the coins and the table: Put 10 of the coins on the table. Say for example that 3 of them are heads. This means there are 7 tails on the table, and on the floor there are 7 heads and 3 tails. So just turn over all of the coins on the table! Now 7 heads are on the table and 7 heads are on the floor. Also well done to Alyzarin for getting the hardest bit of the prisoner puzzle, which is probably the hardest puzzle so far. There's still a little problem, though: what if the light is on at the beginning? Then the counter would turn it off and count it as a prisoner. But then he'd prematurely tell the warden they'd all been. Dianeva, given the way I phrased the question, I believe that's a fair answer. Clever. The warden could easily break it of course, if he were so inclined, by never selecting one of the prisoners on their day, for instance. But I did say he did it randomly, so you could be certain that eventually he would choose the prisoner on their day. How about a very slightly different puzzle where the warden can do such things; the only thing he promises is that each prisoner can always be sure he'll take them to the bathroom eventually (including if they've been before). Alyzarin's solution goes a long way to solving this but isn't quite there. Edit: Thanks Snowycat for the new riddle. Unfortunately I've seen it before, but it's a nice one!