A regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games played decreases by 1/2. Find a rule for the number of games played in the nth round, then find the total number of games played in the regional soccer tournament.

Question

anonymous · Answer

first : 2^5 or 2^ 6-1

second: 2^4 or 2^ 6-2

nth: 2^ 6-n


last : 2^ 6-6  = 1  implies sixth round == final match