Friday, 26 December 2008

The Queen 5x5 Puzzle - Albert Frank

On a chessboard 5x5, how to put five white queens and three black queens such as no queen can be taken in one move by an opposite colour queen?


According to Albert Frank there appears to be a poor correlation between chess playing strength and the ability to solve this problem. Among non chessplayers, at Glia Society level, Albert predicts about 50% would solve this puzzle.

This problem is also known as the non-dominating queens puzzle.

Personally I did not find this puzzle too difficult, but I don't think it is particularly testing practical chess playing ability. The puzzle seems to be more a test of spatial ability and logic. I have previously discussed the research study by
Waters, Gobet & Leyden (2002) "Visuospatial Abilities Of Chess Players" (here). In this study it was concluded that for adults " ... visual memory ability, and perhaps visuospatial intelligence, may be relatively unimportant factors in the long-term acquisition of chess skill." The lack of correlation between chess playing skill and the apparent ability to solve the above puzzle (as reported by Albert Frank) supports the results of the study by Waters et al (2002). I suspect the conclusions may be different, however, if young gifted chess players are studied (i.e. Frydman & Lynn, 1992).

Albert Frank is a retired Belgian Professor and a member of numerous high IQ societies, he is also a very keen chess player. In 1973 he was involved in a very instructive study looking at chess and academic aptitudes in Zaire school children. The control group students were taught mathematics for 7 hours per week. The experimental group students were taught
the same mathematics program in 5 hours per week with an additional 2 hours per week of chess tuition (by Albert Frank). The experimental group students showed significant improvements in arithmetic aptitude (p=0.05) and verbal logic (p=0.01). A summary of the study is published on Albert Frank's website here. The completed study was published in the book:
Albert Frank,
American Chess Foundation,
December 1978.

Frank, A., & D’Hondt, W. (1979).
Aptitudes et apprentissage du jeu d’échecs au Zaire [Aptitudes and learning of the game of chess in Zaire].
Psychopathologie Africaine, 15, 81-98.

Frydman, M. & Lynn, R. (1992).
The general intelligence and spatial abilities of gifted young Belgian chess players.
British Journal of Psychology, 83, 233-235.

Waters A.J, Gobet F, Leyden G. (2002)
Visuospatial abilities of chess players.
British Journal of Psychology, 93:(4), 557-565

If anyone would like the solution to the above puzzle I am happy to email this to you.

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