lgbasallote
There are 13 teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they all play without any team playing more than one game a day
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Rohangrr
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6 and a half days!
lgbasallote
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1) that's not correct
2) this doesn't have an "LGBARIDDLE" heading so im asking for solution
Rohangrr
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|dw:1348374494350:dw|
pizzapi
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13!/[(13-2)!2!]
pizzapi
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i think that's right, but let me double check
kulprit
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18 DAYS
pizzapi
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yep, 13C2
pizzapi
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all possible ways to choose 2 team out of 13
lgbasallote
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how are you all getting those?
lgbasallote
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and i've tried 13C2 @pizzapi it's not that
nphuongsun93
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12 days. <-'
I guess
lgbasallote
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no. it's supposed to be 13 gamedays with 6 games each. but i don't know how
lgbasallote
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13C1?
pizzapi
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wait, so all the teams play 6 games each?
lgbasallote
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i have no idea. i suppose it means each day has 6 games
pizzapi
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13C2 divided by 6
pizzapi
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since 6 games per day
lgbasallote
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but how do you know 6 games per day?
lgbasallote
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it wasn't given
panlac01
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pay attention: What is the minimum number of days can they all play without any team playing more than one game a day?
pizzapi
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6 teams can play 1 game everyday
pizzapi
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that's the maximum possible games
pizzapi
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per day
lgbasallote
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it's looking for minimum though
pizzapi
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no, its 13 days, with 6 games per day
pizzapi
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because a maximum of 6 games can be played per day
pizzapi
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12 teams can play 6 games on day 1
repeat for day 2
etc.
lgbasallote
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i still don't get the logic why that's the solution
pizzapi
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total games=13C2
pizzapi
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maximum games per day=6
ganeshie8
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im getting 12 days :
first team finishes all its games(12) first day,
second team finishes all its remaining games(11) second day,
...
12+11+10+9+8+7+6+5+4+3+2+1
pizzapi
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minimum days=total games/max games per day
pizzapi
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@ganeshie8 each team can only play 1 game for day
pizzapi
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*per
lgbasallote
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if you divide total by max..won't that make the final answer max?
ganeshie8
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oops ! bad logic disregard that
pizzapi
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no cuz the minimum would be 1 game per day
pizzapi
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you are trying to minmize the number of days, by fitting the most games in one day
panlac01
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I don't think you're reading the whole question and given correctly.
lgbasallote
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what dp you mean @panlac01 ?
lgbasallote
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is there a different solution?
lgbasallote
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13C1 gives the same result though...
lgbasallote
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13 teams..one game per day...so 13C1 would make sense right?
pizzapi
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no, there must be a total of 78 games
pizzapi
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13 teams must play all the other teams
lgbasallote
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isn't that what 13C1 means?
panlac01
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with 13 teams, only 12 teams can play in one day
pizzapi
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no 13 C 1 means the number of ways you can select 1 team from 13 teams
panlac01
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the question is, what is the minimum day that they can ALL play without any team playing more than 1 team a day
lgbasallote
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so what are you implying?
pizzapi
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12 team playing on 1 day=6 games in total for the day
lgbasallote
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this was a question in a board exam back in '94 so it's meant to be tricky
panlac01
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in the first day, you are left with one team unable to play
panlac01
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so you need to move on to the second day to give that specific team who didn't play to play.
lgbasallote
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i really think 13C1 makes sense
lgbasallote
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in the case of (13C2)/6...why divide by 6? of all the numbers?
pizzapi
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6 is the number of games played in 1 day by 12 teams
lgbasallote
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but what about for the case of 13 teams?
pizzapi
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only 12 teams can play per day because they have to be grouped in teams of 2
lgbasallote
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i don't think that means the other team should be disregarded
pizzapi
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its a 1v1 match, 2 teams per game
pizzapi
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okay, on the first day
team 1 vs 2
3 vs 4
5 vs 6
7 vs 8
9 vs 10
11 vs 12
the 13th team can't play because all the other teams have already played a game
lgbasallote
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yes i get that. but im asking for the case of 13 teams. is that logic applicable in that case?
lgbasallote
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you used 13C2 and then divided by 6 (which is for 12 teams)
pizzapi
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13C2 represents the total games because you are select teams of 2 out of 13 teams
if you organize all the games, 6 games per day, it would take 13 days in total
pizzapi
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*groups of two teams out of 13 teams
panlac01
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so what is the answer with the formula being suggested?
panlac01
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ganesh is close
pizzapi
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(13C2)/6
I really need to work on explaining things, hopefully openstudy will help me with that
panlac01
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don't worry bro, you got it from the first time. Illustration makes a better explanation sometimes.
lgbasallote
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so do you agree with pizzapi already @panlac01 ?
PhoenixFire
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@pizzapi Is right. Because there has to be a total of 78 games played for each team to play each other team. It asks for the minimum number of days for these 78 games to be played in (at least that's the interpretation of the question). So to find that you divide 78 by the maximum number of games that can be played on a single day, which is 6.
Therefore, 78/6=13. It takes 13 days for all teams to play each other.