Sunday, September 20, 2009

Knights and Knaves solutions

See the original puzzles

Classic #1:

"Which way to your village?" Take that path.

Classic #2:

"Which way would your sister say is the way out?" Take the other path.

I suppose for either of these classics, you could simply ask, "What you say if I asked you which is the right way?" But that's not as clever IMO.

Bonus Problem:

This one involves some complicated reasoning. I'm going to break it down into steps.
  1. I look at the pointing fingers, and there is not a single person who is certainly a knight or certainly a knave. But I do know there is at least one knight at the table.
  2. Consider a single person. Given my current knowledge, it is possible that he is a knight.
  3. If that person is a knight, then he is pointing to the next knight on his left, who is pointing to the next knight on his left, and so on, until we complete the loop of knights around the table.
  4. Each person at the table must be part of exactly one such loop.
  5. Because I could determine how many knights are at the table in total, then all possible loops must have the same number of people.
  6. There are 25 people at the table. 25 is the product of the number of loops by the number of people in each loop.
  7. Because no one pointed to themselves, the loops must have more than one person each.
  8. You can't just have one loop which includes everyone at the table, since then I would know for sure that everyone is a knight.
  9. Therefore, there are five loops of five each. One of those loops consists of knights, while the others consist of knaves. There are five knights total.
I thought it was pretty clever problem myself. I'm happy I can write these fiendishly difficult problems and still have them solved by one or two readers out there.

1 comment:

Secret Squïrrel said...

Miller, you have every right to be proud of yourself. The bonus problem was a really nice take on the classic.