Question

How many hockey teams could play in a 100 round single-elimination hockey tournament? Los Angeles Vancouver Los Angeles Toronto Toronto St. Louis Los Angeles Montréal Pittsburgh New York Tsi. New York Isl. Montréal Montréal Buffalo Round 1 Round 2 Round 3

Answer 1

As we can see in the above picture that the number of teams in each round is of the form 2^k where k is the (number of rounds - current_round number +1)

We can confirm this as in round 1 8 teams are playing thus 8 = 2^k

k = 3

number_of rounds = 3

current_round_number = 1

therefore, number_of_rounds - current_round_number + 1 = k

In round 2

k = 2

number_of_rounds - current_round_number + 1 = k

3 - 2 + 1 = 2

L.H.S = R.H.S

Therefore total number of teams that can play in 100 rounds tournament = 2^{100 - 1 + 1} = 2¹⁰⁰ = 1,267,650,600,228,229,401,496,703,205,376 teams.