Rabbi Aaron Kotler, the famous Rosh Yeshiva, used to set puzzles for prospective students at his Yeshiva to test what we today call their IQ. One of these was: prove which of the following two statements is true and which is false. (1) No two people on earth have exactly the same number of hairs on their head. (2) There are people on earth with exactly the same number of hairs. The proof that (1) is false is, of course, that since there are billions of people on earth it is impossible for everyone to have a different number of hairs - that would mean that there are people with millions of hairs on their head and clearly there are no such people.A similar puzzle which I heard had been set by R. Aaron Kotler to test his student' ability to deal with problems was already familiar to me from the 'Japes and wheezes' column in my boyhood comics. A lily pond doubles itself each day and in 28 days the pond is full. How long does it take for the pond to be a quarter full? The answer is, of course, 26 days, not, as most people reply, seven days.
In Helping With Inquiries; An Autobiography (London, 1989) by Louis Jacobs, pg. 72.
 Actually I have no idea if this was in Lakewood, or Kletzk. See this post about R. Haim Joseph of Baghdad's brain teasers for sharpening the mind of youths.