In a chess tournament , each of two players have only one game played. After 2 rounds 5 players left the tournament. At the final of tournament was found that the number of total games played is 100. How many players were at the start of the tournament?
Problem
Source: Moldova MO 2007 10.5
Tags: combinatorics
ftre775
28.01.2019 21:21
Bump????
qwerty123456asdfgzxcvb
28.01.2019 21:26
105......
ftre775
28.01.2019 21:27
Proof????
qwerty123456asdfgzxcvb
28.01.2019 21:38
well there's 100 players now and 5 players left, so there is 100+5=105 players at start
Pi_
29.01.2019 03:09
qwerty123456asdfgzxcvb wrote: well there's 100 players now and 5 players left, so there is 100+5=105 players at start It says there were 100 games played, not 100 people now
qwerty123456asdfgzxcvb
29.01.2019 04:47
Oh. Well then everyone plays games against every other person, so c(2,n), but when do the 5 players leave? define "round" in this problem
Math-Ninja
29.01.2019 04:57
Is this a 1 v 1 elimination tournament?
ftre775
29.01.2019 08:01
qwerty123456asdfgzxcvb wrote: Oh. Well then everyone plays games against every other person, so c(2,n), but when do the 5 players leave? define "round" in this problem Round is not defined.
ftre775
29.01.2019 08:03
Math-Ninja wrote: Is this a 1 v 1 elimination tournament? This is not defined.
WolfusA
29.01.2019 15:54
I think round is just a set of matches between paired players
qwerty123456asdfgzxcvb
02.02.2019 00:21
When do the players leave?
ftre775
05.02.2019 11:58
qwerty123456asdfgzxcvb wrote: When do the players leave? The players leaves after 2 rounds
qwerty123456asdfgzxcvb
12.02.2019 03:20
What is a round???