A game is played between 2 players and one player is declared as winner. All…
2023
A game is played between 2 players and one player is declared as winner. All the winners from first round are played in second round. All the winners from second round are played in third round and so on.
If 8 rounds are played to declare only one player as winner, how many players played in first round?
- A.
256
- B.
512
- C.
64
- D.
128
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept: In a single-elimination knockout format, every game is played between exactly 2 players and produces exactly 1 winner, so each round exactly halves the field. If a tournament runs for r rounds before one champion remains, the number of players who started round 1 is 2 raised to the power r.
Application: Work backward from the final (8th) round, doubling the player count one round at a time, since each round's players are exactly twice the number of winners it produced:
Round 8 (final round): 2 players play, producing 1 champion.
Round 7: 2 × 2 = 4 players (they produced the 2 winners who entered round 8).
Round 6: 4 × 2 = 8 players.
Round 5: 8 × 2 = 16 players.
Round 4: 16 × 2 = 32 players.
Round 3: 32 × 2 = 64 players.
Round 2: 64 × 2 = 128 players.
Round 1: 128 × 2 = 256 players.
Cross-check: Starting forward from 256 players in round 1 and halving at every round — 256 → 128 → 64 → 32 → 16 → 8 → 4 → 2 → 1 — takes exactly 8 halving steps to reach a single champion, confirming the count.
Hence, 256 players played in the first round.