A game is played between two players and one player is declared as winner .…
2026
A game is played between two players and one player is declared as winner . All the winners from first round, played in the second round . All the winners from second round played in third round and so on . If 8 rounds were played to declare only one player as winner , how many players played in first round ?
- A.
230
- B.
260
- C.
256
- D.
273
Attempted by 1079 students.
Show answer & explanation
Correct answer: C
Key idea: Each round halves the number of players until only one winner remains.
Step-by-step reasoning:
Let x be the number of players in the first round.
After 1 round: x/2 players remain. After 2 rounds: x/4. After n rounds: x/2^n.
After 8 rounds there is 1 player, so x/2^8 = 1.
Therefore x = 2^8 = 256.
Answer: 256