Mathematical recreations and essays . rring again when the system is rotated course a vertex cannot be at the point 1 or y, as thesepoints will be required for the diameter triplet {\. k. y). These remarks will be clearer if we apply them to a definiteexample. I take as an instance the case of 15 girls. As beforewe represent 14 of them by equidistant points numbered 1, 2,3, ... 14 on the circumference of a circle, and one by a point kat its centre. Take as one triplet the diameter (1. k. 8). Thenthe sides p, q, r may have any of the values [1], [2], [3], [4], [5],[6], and each va
Mathematical recreations and essays . rring again when the system is rotated course a vertex cannot be at the point 1 or y, as thesepoints will be required for the diameter triplet {\. k. y). These remarks will be clearer if we apply them to a definiteexample. I take as an instance the case of 15 girls. As beforewe represent 14 of them by equidistant points numbered 1, 2,3, ... 14 on the circumference of a circle, and one by a point kat its centre. Take as one triplet the diameter (1. k. 8). Thenthe sides p, q, r may have any of the values [1], [2], [3], [4], [5],[6], and each value must be used twice. On examination it willbe found that there are only two possible groupings, namely[1, 1, 2], [2, 4, 6], [3, 3, 6], [5, 5, 4], and [1, 2, 3], [1, 4, 5],[3, 5, 6], [2, 4, 6]. One of the solutions to which the first set ofgroupings leads is defined by the diameter (1. k. 8) and the fourtriplets (9. 10. 11), (4. 6. 14), (2. 5. 13), (3. 7. 12); see figure ii,below: of the four triangles used three are isosceles. The. FI (jure iL
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