Here is a question I found on the Mensa website under “Mensa Workout”:
Sally likes 225 but not 224; she likes 900 but not 800; she likes 144 but not 145. Does she like 1600 or 1700?
The pattern the question designers “want” me to find is that Sally likes perfect squares, and so she likes 1600. But there seems to be other valid solutions:
1. Sally likes 1700 because she likes the roots of x4 – 2969 x3 + 2521800x2 – 648810000 x + 49572000000, which is 144, 225, 900 & 1700. [I have to confess that I used Maxima to arrive at this solution. But I bet a pencil and paper is all one needs to expand (x – 1700) (x – 900) (x – 225) (x – 144) ].
2. Sally likes 1600 because she likes the roots of x4 – 2869 x3 + 2394900x2 – 612360000 x + 46656000000
3. (This one is for the fans of Occam’s Razor) Sally likes numbers whose sum of the digits is odd. Therefore she likes 1600, not 1700.
4. Sally likes numbers in which the sum of the digits plus the number of digits equals 12. Therefore, she likes 225, 900, 144, and, of course, 1700.
5. Sally does “not” like 1600 or 1700, because neither number has digits which sum to 9. She “does”, however, like 1800.
All these solutions are logical but only 3 out of these 6 rational solutions gives me a score.
All this makes me wonder: Is Intelligence test scores a social phenomena? Please note the fact the these questions are designed by people who are recognized by the society as intelligent, i.e people who have achieved something “great” in their lives. That implies that the society defines somebody as “intelligent” just because he thinks “like” the other “great” people.
What if Beethoven was born before the piano? Spielberg before the invention of the camera? Steve Jobs before the computers? So there are people alive today whose technology have not yet been invented, the perfect means to their genius has never materialized. And if society starts to brand, recognize and promote only the people who are like the achievers of yesterday, I think we will soon enter a second Dark Age.