Segar. — A Note on Drawing for Competitions. 503 



Table I. 

 Scheme of Matches between Seven Competitors. 



Thus, e.g., in the first round 1 has a bye, 2 (at home) 

 plays 7 (away), 3 (away) plays 6 (at home), and 4 (at home) 

 plays 5 (away). 



Table II. 



If this rule were adopted the only drawing necessary would 

 be for the numbers to represent the several clubs, everything 

 else would then follow. 



It has already been mentioned that it is impossible to com- 

 pletely achieve this arrangement in the case of the number of 

 clubs being even. The nearest approach that is possible ap- 

 pears to be as follows : — 



Write down columns as in the case above of an odd num- 

 ber of clubs, taking the odd number which is one less than the 

 actual number of clubs. Then take the even number repre- 

 senting the number of clubs and write it at the side of each of 

 the solitary numbers in the first row, but alternately on the 

 right and on the left of them consecutively. The several 

 columns then represent, as before, the competing clubs for the 

 successive rounds, each club playing every other once. There 

 are, of course, no byes. 



If, further, we subscribe "h" and "a," with the same 

 meanings as before, to the numbers in each column alter- 

 nately, descending with the numbers on the left and rising 

 with those on the right, we get the home club indicated for 



