Mind Bender # 12: Anyone for Tennis?
The way things are shaping up, there could be a record number competing in this year’s Australian Open — some 803 players in all.
The break-up looks like being:
- 457 male players, and
- 346 female players
So, the question is …
How many games in total do the organizers need to schedule, in order to obtain a result for both the Male and Female Crowns?
And make sure you fully detail, just how you arrived at your solution.
8 November, 2007 at 10:49 am
801 - If you lose your out, so there needs to be 801 losers to get the last one standing.
8 November, 2007 at 11:05 am
I have assumed the question is really asking how many matches. Each player except the winner of each group loses one match and each match eliminates one player, so one less match than the number of players must be played in each group. Therefore there are 456+345= 801 matches.
8 November, 2007 at 11:11 am
Since there only needs to be one remaining player, there needs to be 456 mens matches, and 345 female matches, whereby one player is eliminated each match!
No calculations necessary!
8 November, 2007 at 11:34 am
They would need to schedule 801 games,
As there are 803 player in total and they want a Male and a Female winner, there would have to be 801 players that lose, therefore they would need 801 games (matches) to acheive that.
8 November, 2007 at 12:23 pm
Total 802
My assumption is all players must play in each round.
games players remain games players remain
457 0 346
Round 1 229 228 173 173
Round 2 114 114 87 86
Round 3 57 57 43 43
Round 4 29 28 22 22
Round 5 14 14 11 11
Round 6 7 7 6 5
Round 7 4 3 3 2
Round 8 2 1
456 346
Mens Womens
8 November, 2007 at 12:53 pm
449 games for the guys and 345 games for the gals
a total of 794 games
worked it out on a spreadsheet
allowing everyone at least one game
8 November, 2007 at 2:09 pm
Something went wrong with format.
Try again.
Mens.
games players remain
457
Round 1 229 228
Round 2 114 114
Round 3 57 57
Round 4 29 28
Round 5 14 14
Round 6 7 7
Round 7 4 3
Round 8 2
Total 456 games.
Womens
games players remain
0 346
173 173
87 86
43 43
22 22
11 11
6 5
3 2
1
Total 346 games
Grand total 802 games
10 November, 2007 at 7:55 am
The answer is 2.
The finals are the only two games which need to be scheduled which will provide the result. All the rest need to be scheduled but do not in and of themselves provide a result to the tournament.