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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 THE SWITCH WILL BE IN THE OFF POSITION. AFTER SWITCHING 4 TIMES, THE SWITCH WILL RETURN TO ITS ORIGINAL POSITION. SO, 3922 / 4 = 980 WITH REMAINDER 2. THE SWITCH WILL BE AT MEDIUM POSITION AFTER SWITCHING 3920 TIMES, AND AT OFF POSITION AFTER ANOTHER 2 SWITCHES 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 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