Draw lots!
I鈥橫 sure that you are all very familiar with those football league tables, which have columns showing the number of matches won, lost and drawn by each of the teams, together with information on goals for and against, and points scored. This little problem concerns the 鈥渕atches drawn鈥� column in a league table in which each of the teams has played each other team only once.
In a league with four teams, there are 54 possible arrangements for this column, starting with 0,0,0,0, (no matches drawn) and ending with 3,3,3,3 (all 6 matches drawn), and assuming that different combinations of the same digits 鈥� such as 1,1,2,2 and 1,2,1,2 and 2,2,1,1 etc 鈥� are all counted.
Advertisement
My question is how many such arrangements are possible in a league with five teams?
A 拢10 book token will be awarded to the sender of the first correct answer opened on Thursday 23 November. The Editor鈥檚 decision is final. Please send entries to Enigma 845, New 杏吧原创, King鈥檚 Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 839 was B.T. Legesse of Addis Ababa, Ethiopia.
Answer to Enigma 839
Squash square
A and E tie