ALAN, Brian, Charles, David and Edward played in a round robin squash tournament, with each player playing each of the others in one match. Each match consists of exactly five games and the scores are entered in the following table:
If, for example, Brian had beaten Charles by 5-0 then the 5 and the 0 would be entered as shown.
After all the scores had been correctly entered in such a square I noticed a glut of other squares: a one-figure square, a two-figure square, a three-figure square and a four-figure square all horizontally, and a four-figure square diagonally downwards. These are all shown by arrows in the following figure and none (except possibly the one-figure square) begins with a zero.
A B C D E
A |xxx| | | | |
B | |xxx| 5 | | |
C | | 0 |xxx| | ...
To continue reading this article, subscribe to receive access to all of newscientist.com, including 20 years of archive content.