Martin Joos, Head of the Dept. of Germanic L & L, UW, Madison, WI, freaked out his entering graduate students by administering little tests upon meeting them for the first time; he was not so much interested in their smarts as their problem-solving personality type (in his typology). Example: he would write down the first few odd numbers, "1 3 5 7 9 ..." Then he would reckon out loud, "1 plus 3 is 4, plus 5 is 9, plus 7 is 16... What is the sum of the first 60 odd numbers?" His typology, based on the response:
Type I. Defense, anger, refusal.
Type II. Collapse.
Type III. "Oh, yeah, we had a formula for this in school..." (Needless to say, he didn't care if they could remember a formula or come up with an answer.)
Type IV ("Engineers"). They'd think a few seconds and then answer, "3600."
Type V ("Mathematicians"). They'd answer instantly, "360."