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 Forum index » Archive » Archive: Perplex City » PXC: Puzzles
pxc newsletter puzzle
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bowkar
Greenhorn


Joined: 19 Apr 2006
Posts: 5
Location: guildford uk

 		pxc newsletter puzzle
Quote:
World Cup Fever is currently gripping the... uh, world, and if not theworld, then at least a decent proportion of the Mind Candy staff. 32teams are competing for the trophy, but we don't reckonthat's nearly enough. In fact, if we organised it, there'd be 314 teams- something of a lucky number - and none of this "group stage" nonsense.Why settle for a draw when you can have the drama of extra time, suddendeath and penalty shootouts? Yes, in *our* version, every match would bea straight knockout, with the losing squad exiting the tournament aftereach match. The question is, then - how many matches would need to be played to findour champion?


Spoiler (Rollover to View):
if there are 314 teams there must be 157 games and 157 winners.
but 157 teams can't all play in the next round as 157 is an odd number


so i'm stuck on this already!
can this be a mistake or am i missing something fundamental here?

PostPosted: Tue Jun 20, 2006 7:35 am
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Talon
Boot


Joined: 06 May 2006
Posts: 54
Location: Washington, USA

 		Well, if you want to be a bit unfair...

Spoiler (Rollover to View):
Have 116 teams play, you get 58 winners. Add 58 to the 198 who haven't played yet and you have 256, then it's just a matter of halving them each round 'til you're down to 1. I'm sure there's an actual way to do it evenly and fairly, but math is not my strong point by any means.


As to how to actually do it within the confines of a knockout tournament... no idea. Again, math is not my strong point.

PostPosted: Tue Jun 20, 2006 7:58 am
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Gibbet
Veteran


Joined: 07 Aug 2005
Posts: 121

 		A little nudge for those who are stuck:

Spoiler (Rollover to View):
It's not the winners that are important.

_________________
"And I would have got away with it if it wasn't for those pesky cards!"

The OK13DTFC is but one of the things i'm ashamed of being associated with!

PostPosted: Tue Jun 20, 2006 8:53 am
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bowkar
Greenhorn


Joined: 19 Apr 2006
Posts: 5
Location: guildford uk

 		dont tell me
Spoiler (Rollover to View):
it's the taking part that counts?

and i'm still stuck

PostPosted: Wed Jun 21, 2006 12:01 pm
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UKver2.0
Decorated

Joined: 09 Feb 2006
Posts: 270

 		Nope. He's just hinting at the easy (short-cut) way of solving this.

Spoiler (Rollover to View):
Every game produces one winner and one loser. "It's not the winners that [count]."


We should have a weekly poll for these with voting choices red - silver. I'd call this an orange.

PostPosted: Wed Jun 21, 2006 12:37 pm
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Scott
Entrenched


Joined: 11 Sep 2004
Posts: 1140
Location: 390 Chestnut Ridge Rd, Rochester NY, 14624, USA

 		I would've thought this would be pretty simple. The trick is, I suppose, knowing what to do with odd numbers. In sporting events like this, teams are paired up in twos. But when there is an odd number of teams, that team gets a fFree ride fFor the week. This is sometimes referred to as a Bye (Apparently a Bye is something else in cricket, butI'm afraid I don't know cricket very well).

(a slightly more detailed breakdown fFollows)
Spoiler (Rollover to View):
If we have 4 teams, we would break them up into pairs of 2. That will give us 2 games. Then the winner of each of the two games will play in a third game. In this case we have 314 teams. So we break them up into 157 pairs. That will give us 157 games. then the 157 winners pair off (plus one bystander) and play 78 games, for a running total of 235 games played.

I won't give you the answer, but i will show you a nice way of coming up with an answer. Toss these values into a spreadsheet, with the "314" being in cell A1

314
=INT(A1/2)
=INT(A2/2)
=INT(A3/2)
=INT(A4/2)
=INT(A5/2)
=INT(A6/2)
=INT(A7/2)
=INT(A8/2)
=SUM(A2:A9)


cheers Smile
_________________
Perplex City is a game whose only rule is: There must be a party.
Balance of Powers is a game whose only rule is: There must be a political party.

PostPosted: Wed Jun 21, 2006 4:27 pm
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e_nygma
Decorated

Joined: 17 May 2006
Posts: 247
Location: Maryland, US

 		This may be me reading something implicit in the question, but I get the feeling that there are no byes. If MC is objecting to group play, how would they condone a bye? This is a pure "play and stay" tourney, so no free rides.

PostPosted: Wed Jun 21, 2006 7:10 pm
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UKver2.0
Decorated

Joined: 09 Feb 2006
Posts: 270

 		I'm guessing Scott actually summed the infinite series for #109. Razz and still got it wrong. What becomes of the .5 you keep dropping? Don't they get a chance to play? Sad

All you have to do is
Spoiler (Rollover to View):
Count the number of losers. Once you lose you are out and there are no ties. One game per loser. One winner.


Good luck with the "no byes" thing.

PostPosted: Wed Jun 21, 2006 7:50 pm
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obrienk
Veteran

Joined: 28 Jun 2006
Posts: 73

 		Re: pxc newsletter puzzle
bowkar wrote:
Quote:
World Cup Fever is currently gripping the... uh, world, and if not theworld, then at least a decent proportion of the Mind Candy staff. 32teams are competing for the trophy, but we don't reckonthat's nearly enough. In fact, if we organised it, there'd be 314 teams- something of a lucky number - and none of this "group stage" nonsense.Why settle for a draw when you can have the drama of extra time, suddendeath and penalty shootouts? Yes, in *our* version, every match would bea straight knockout, with the losing squad exiting the tournament aftereach match. The question is, then - how many matches would need to be played to findour champion?


Spoiler (Rollover to View):
if there are 314 teams there must be 157 games and 157 winners.
but 157 teams can't all play in the next round as 157 is an odd number


so i'm stuck on this already!
can this be a mistake or am i missing something fundamental here?


without reading the thread, i reckon it must be
Spoiler (Rollover to View):
313 games. in that there needs to be 313 losing teams, and one winner


PostPosted: Sat Aug 12, 2006 10:13 am
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