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Counting Lines and Planes in generalised noughts and crosses

Published online by Cambridge University Press:  22 September 2016

Paul Taylor
Paul Taylor*
Affiliation:
Royal Grammar School, High Wycombe, Bucks
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Extract

In the familiar [32] game of noughts and crosses or ticktacktoe, there are eight ‘winning’ Lines. These are the lines having the maximum number, 3, of Points in a 3 × 3 lattice, as in the figure.

Type
Research Article
Information
The Mathematical Gazette , Volume 63 , Issue 424 , June 1979 , pp. 77 - 82
Copyright
Copyright © Mathematical Association 1979

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References

‡ The convention will be adopted that ‘Line’ will mean a line with the maximum number, k (in this case 3), of points. Similarly ‘Plane’ will denote a plane having k2 (or in general kr in r dimensions) points. In the same way, ‘Point’ will indicate a lattice point.