Enigma 249: Championship double
9 January 2015
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From New Scientist #1396, 9th February 1984 [link]
We are drawing up plans for our local club’s annual tennis championship for the next few years. The championship is held for a week in spring and consists of a group of members each playing each of the others just once. We are planning for increased numbers of participants and so we asked the groundsman how many matches the courts could cope with in this and next year’s championships. He gave his figure for this year and said that with the planned club extensions we could cope with twice that figure next year.
The chairman reacted that both those figures were inappropriate as neither equalled a possible “championship total” number of matches, that is to say no matter how many players took part in a championship the number of matches needed could not equal either of the groundsman’s estimates.
So the chairman interpreted these figures by assuming that the number of matches played this year and next would be the lowest “championship totals” above each of the groundsman’s estimates. He then announced his revised estimates for this year’s and next year’s matches and, by coincidence, his figure for next year is twice his figure for this year.
One might be led to believe that the year after next will see three times the number of matches which the chairman predicts for this year; but that is impossible. But it could happen that the number of matches in the championship they year after next is three times the groundsman’s estimate for this year.
How many matches did the groundsman estimate for this year?