**From New Scientist #2507, 9th July 2005**

All the teams in our area have until now been divided up into a number of identical local leagues, but from next season they will come together to play each other in an area league in which each team will play each of the other teams once. All matches will be completed in less than a year even though each team will play on average less than one match a week.

The number of teams that will be promoted from the area league at the end of the season has not yet been decided. The number of different combinations of teams that could be promoted if four teams are promoted is a multiple of the number of different combinations of teams that could be promoted if three teams are promoted, and the latter number is itself a multiple of the number of different combinations of teams that could be promoted if two teams are promoted.

How many teams will be in the area league?

[enigma1348]

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Solution:There will be 35 teams in the area league.