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.

I'm a programmer and it seemed like the obvious choice was "2". It is right there are the start of the list! Was there some indication that the individuals were given different (ie. shuffled) lists? If they were shuffled or, say, provided as a heap of cards with numbers on them it may be slightly more credible "eye of the beholder" scenario.