Two people are separately confronted with the list of numbers [2, 5, 9, 25, 69, 73, 82, 96, 100, 126, 150 ] and offered a reward if they independently choose the same number. If the two are mathematicians, it is likely that they will both choose 2—the only even prime. Non-mathematicians are likely to choose 100—a number which seems, to the mathematicians, no more unique than the other two exact squares. Illiterates might agree on 69, because of its peculiar symmetry—as would, for a different reason, those whose interest in numbers is more prurient than mathematical.

This is a trivial point, but as a student of mathematics, I feel compelled to point out that while I think he is correct that most mathematicians would choose 2, his reasoning for why is wrong. Mathematicians would pick 2 because there is a convention in mathematics of, when you have to make an arbitrary choice (but want to specify it anyway), pick the smallest (if this makes sense in context).