THOG problem

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The THOG problem is one of Peter Wason's logic puzzles, constructed to show some of the weaknesses in human thinking.


You are shown four symbols

  1. a black square
  2. a white square
  3. a black circle
  4. a white circle

and told by the experimenter "I have picked a colour (black or white) and a shape (square or circle). A symbol that possesses exactly one of these properties, is a THOG. The black circle is a THOG. What can be said about the other symbols? Which one is the symbol I picked, or THOG, not-THOG, or undecidable?"

Presented in this form, the task is quite difficult, because much information must be held in working memory at the same time. A first step towards a solution is rephrasing the first sentence of the experimenter's statement to "I have picked one of the symbols". It cannot be the black circle, which, being a THOG, possesses only one of the required properties. The chosen symbol must be the black square or the white circle. The white square, being the "opposite" of the black circle, also has exactly one of the required properties, making it a THOG.