The Lemon Fool

If Cinelli can post a problem from a newspaper, then so can I. This one came to me through a feed, and I like it. Oxford University entrance questions, that I'm sure regulars here will find as straightforward as I did.

I'm not going to try and represent them here: rather I'll give the URL below. But they do raise some supplementary points that might merit discussion, though mostly I expect regulars here will enjoy the puzzles themselves.

1. Stephanie's Surprise
In the first puzzle, what assumptions are made about the order in which the participants speak?
Reverse the order and you get a different outcome, and need a more involved observation from R before C can know the answer. But for supplementary question (c) it's not obvious to me how they expect that to be tackled.

2. Tile Party.
(a) Why is this puzzle logically flawed all the way through?
(b) It relies on a particular convention. How, by applying another convention of such puzzles, could we solve it instantly?

3. Alice's Boxes. (also even more pedantically applies to 1, but not to 2).
What, pedantically speaking (but crucially to a pedant), is missing from the formulation of the question?

The URL is https://www.theguardian.com/science/202 ... -questions

There is always a question of the motivation and truthfulness of all participants. Including the person who says Stephanie, Coleen et. al. are perfectly logical, and did not, but probably would if pressed, say they are truthful.

9873210 wrote:There is always a question of the motivation and truthfulness of all participants. Including the person who says Stephanie, Coleen et. al. are perfectly logical, and did not, but probably would if pressed, say they are truthful.

Hmmm, I wasn't thinking of that as an element in the problem. Though I guess my mention of pedantry invites your comment. My pedantic point was rather different, and it jumped out at me only in problem 3 despite being shared by problem 1.

The issue that most struck me is the quantum of time. Epistemologically, your fellow-player's silence conveys information, as does your own silence. After two quanta of silence, both players know the answer. The convention of the quantum is horribly violated by the second problem describing "long, awkward silence" before anyone infers any information. Whoever imported those adjectives should be fired!

Indeed, problem 3 would be clearer if both people responded "no!" as soon as the question was asked.

But these kind of questions about "knowledge about knowledge" can be rather mind-bending, especially as the number of levels increases. I seem to remember something over on Motley Fool about an island and eye colours that created a never-ending and highly controversial thread...

If you really want to bend your mind - https://en.wikipedia.org/wiki/Unexpecte ... ng_paradox