This kind of reminds me of the 'Mr. P and Mr. S' puzzle.

In case you don't know it, there are two numbers (m,n) between 1 and 100. Mr. P is told the product (m * n) and Mr. S is told the sum (m + n), but neither is told the original numbers.

Then they have a conversation that goes like this:

Mr. P: I don't know what the numbers are.

Mr. S: I knew you didn't know them. I don't know them either.

Mr. P: Oh, now I know what they are!

Mr. S: Me too! I know too!

Djikstra's reply is pretty cool: http://www.cs.utexas.edu/users/EWD/ewd06xx/EWD666.PDF

I just solved it in 1,5 hour without using pen and paper at all! But then, I didn't prove it was unique and was kind of lucky the solution was small...

Clarification: the range is _exclusive_. Neither number can be 1.

Ah yes, sorry for not stating the puzzle correctly. That happened when it was explained to me the first time too and I forgot how annoying it is.

Some variations of the problem: http://www.math.uni-bielefeld.de/~sillke/PUZZLES/logic_sum_p...

This is fascinating! I love that the solution requires balancing every answer with every other answer, so that at time it appears nearly solved but one offset number ruins everything else.

The trick is to slowly narrow the choices. After the narrowing, you can start making simplifying assumptions and see if these assumptions are self-consistent with the test. Like a sudoku, but not boring and trivial.

I just read it out too. Amazing creation as a whole.

The toughest thing was i could not scratch out the 'not-possible' options to think more clearly. I took me a little more than an hour.

What a great idea. It may take all my strength to resist getting sucked in, damn you! And I was just telling someone how refreshingly boring Hn has been lately.

Here's a collection of links about the puzzle, including various methods of solution and other self-referential puzzles (the author's link in the article is broken):

http://faculty.uml.edu/jpropp/srat.html

It's an exercise in inductive reasoning to say the least.

So who's going to write a Prolog program to solve this?

This is unnecessary; the solution is fairly straightforward, although it would have been more elegant if the problem constrained question 20 better.

Yeah, but that's no fun ;)

wow - I've got the first few easy ones - but that's getting pretty insane..

How long does it take people to finish?

Took me about an hour or so using only logical reasoning - no guessing.

This is fun. When you are done solving it. Try separating the answers into words. You should end up with an interesting sentence.

I just read that. Wow. That must have taken a while.

~30 mins. Its really a game of organization and considering the possibilities. I think the SRAT should replace IQ tests and the SAT. Just have a set of these in increasing levels of difficulty and grade people by which ones they manage to solve.

It's still only testing the ability to perform a particular test. Intelligence is so much broader and is only generally correlated with these types of logic tests.

Still a massive improvement over the SAT et al. At least we have some correlation.

You don't think there is any correlation at all with the SAT and intelligence? Come on.