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C H _ M P _ _ N Clue
149 (150 - 1) GAMES, SINCE ALL BUT ONE LOSE ONE GAME. TO MAKE IT SIMPLER, ASSUME THERE ARE 3 MEMBERS. ONLY 2 GAMES NEED TO BE PLAYED TO DETERMINE THE CHAMPION THEY STOLE 301 DIAMONDS IN TOTAL. WE NEED A NUMBER THAT IS A MULTIPLE OF 7 THAT WILL GIVE A REMAINDER OF 1 WHEN DIVIDED BY 2, 3, 4, 5, AND 6. THE LEAST COMMON MULTIPLE OF THESE NUMBERS IS 60. SO, WE NEED A MULTIPLE OF 7 THAT IS 1 GREATER THAN A MULTIPLE OF 60. 60 + 1 = 61, NOT A MULTIPLE OF 7 60 X 2 + 1 = 121, NOT A MULTIPLE OF 7 60 X 3 + 1 = 181, NOT A MULTIPLE OF 7 60 X 4 + 1 = 241, NOT A MULTIPLE OF 7 60 X 5 + 1 = 301, A MULTIPLE OF 7 29 MATCHES ARE REQUIRED TO DETERMINE THE WINNER. EVERY TIME A MATCH IS HELD, ONE PLAYER IS ELIMINATED AND TO ELIMINATE 29 OF THE 30 PLAYERS, 29 MATCHES ARE REQUIRED TOM WINS AGAIN. IN THE FIRST RACE TOM RAN 100 METERS IN THE TIME IT TOOK HARRY TO RUN 95 METERS. SO IN THE SECOND RACE WHEN HARRY IS AT THE 95 METER MARK TOM WILL ALSO BE THERE (SINCE 100 - 5 = 95). SINCE TOM IS FASTER HE WILL PASS HARRY IN THE LAST 5 METERS OF THE RACE