Enigma 1169: Snookered
From New Scientist #2325, 12th January 2002 [link]
George lives not far from the Crucible Theatre, where the annual World Snooker Championship has been held for the past 25 years. Each year 32 players compete in a straightforward knockout tournament to determine who is the champion.
George, and his brother Fred, have entered a less prestigious tournament at their local pub. Since they cannot be certain that the number of entrants will be a power of two, lots will be drawn to see who is awarded byes in the first round. The tournament will then continue as a knockout, also drawn at random.
While waiting for the draw to be made, George calculated the chance that he will at some stage have to play against his brother, assuming all the players are of equal ability. It is exactly one in ten.
How many players entered the tournament?