Bongard problem

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An example Bongard problem, the common factor of the left set being convex shapes (the right set are instead all concave).

A Bongard problem is a kind of puzzle invented by the Russian computer scientist Mikhail Moiseevich Bongard (Михаил Моисеевич Бонгард, 1924–1971), probably in the mid-1960s. They were published in his 1967 book on pattern recognition. The objective is to spot the differences between the two sides. Bongard, in the introduction of the book (which deals with a number of topics including perceptrons) credits the ideas in it to a group including M. N. Vaintsvaig, V. V. Maksimov, and M. S. Smirnov.


The idea of a Bongard problem is to present two sets of relatively simple diagrams, say A and B. All the diagrams from set A have a common factor or attribute, which is lacking in all the diagrams of set B. The problem is to find, or to formulate, convincingly, the common factor. The problems were popularised by their occurrence in the 1979 book Gödel, Escher, Bach by Douglas Hofstadter, himself a composer of Bongard problems. According to Hofstadter, "the skill of solving Bongard problems lies very close to the core of "pure" intelligence, if there is such a thing".[1] Bongard problems are also at the heart of the game Zendo.

Scientific works on Bongard problems[edit]


  1. ^ Gödel, Escher, Bach, Douglas Hofstadter, Twentieth anniversary Edition, 1999, Artificial Intelligence: Prospects, p. 662
  2. ^ Harry Foundalis. "Why I stopped working on the Bongard Problems". Retrieved 28 June 2020.

External links[edit]