I have picked one color (black or white) and one shape (square or circle). A symbol that possesses exactly one of the properties I have picked is called a THOG. The black circle is a THOG. For each of the other symbols, is it (a) definitely a THOG, (b) undecidable, or (c) definitely not a THOG?
Cognitive psychologist Peter Wason invented this puzzle in 1979 to demonstrate some weaknesses in human thinking. In pilot studies, 0 of 10 student barristers were able to solve it correctly, with one arguing for more than an hour against the correctness of Wason’s solution. Seven of 14 medical students solved it, taking an average of 6.3 minutes. (“This is quite an impressive result.”) One young doctor solved it in his head in about a minute and said, “I would not let any doctor near me who couldn’t solve that problem.” What’s the answer?
In saying “I have picked one color and one shape,” in effect I am saying, “I have picked one of the symbols.” I can’t have chosen the black circle, because we know that symbol has only one of the required attributes. The symbol I’ve chosen must be either the black square or the white circle. Either way, the white square would match my choice in exactly one particular, so it’s definitely a THOG. If I’ve chosen the black square then the black square has both chosen attributes and the white circle has neither; equally, if I’ve chosen the white circle then the white circle has both chosen attributes and the black square has neither. Either way, neither of these symbols is a THOG. So the white square is definitely a THOG and the other two symbols definitely aren’t.
“In one sense the THOG problem is utterly trivial,” writes Wason. “And yet it is non-trivial in the sense that it is astonishingly easy for some individuals and astonishingly difficult for others. At the very least it does seem a cogent test of formal operational thought in an abstract sphere.” See the link below for more details.
