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

- lgbasallote

- schrodinger

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- anonymous

6 and a half days!

- lgbasallote

1) that's not correct
2) this doesn't have an "LGBARIDDLE" heading so im asking for solution

- anonymous

|dw:1348374494350:dw|

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## More answers

- anonymous

13!/[(13-2)!2!]

- anonymous

i think that's right, but let me double check

- anonymous

18 DAYS

- anonymous

yep, 13C2

- anonymous

all possible ways to choose 2 team out of 13

- lgbasallote

how are you all getting those?

- lgbasallote

and i've tried 13C2 @pizzapi it's not that

- anonymous

12 days. <-'
I guess

- lgbasallote

no. it's supposed to be 13 gamedays with 6 games each. but i don't know how

- lgbasallote

13C1?

- anonymous

wait, so all the teams play 6 games each?

- lgbasallote

i have no idea. i suppose it means each day has 6 games

- anonymous

13C2 divided by 6

- anonymous

since 6 games per day

- lgbasallote

but how do you know 6 games per day?

- lgbasallote

it wasn't given

- anonymous

pay attention: What is the minimum number of days can they all play without any team playing more than one game a day?

- anonymous

6 teams can play 1 game everyday

- anonymous

that's the maximum possible games

- anonymous

per day

- lgbasallote

it's looking for minimum though

- anonymous

no, its 13 days, with 6 games per day

- anonymous

because a maximum of 6 games can be played per day

- anonymous

12 teams can play 6 games on day 1
repeat for day 2
etc.

- lgbasallote

i still don't get the logic why that's the solution

- anonymous

total games=13C2

- anonymous

maximum games per day=6

- ganeshie8

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

- anonymous

minimum days=total games/max games per day

- anonymous

@ganeshie8 each team can only play 1 game for day

- anonymous

*per

- lgbasallote

if you divide total by max..won't that make the final answer max?

- ganeshie8

oops ! bad logic disregard that

- anonymous

no cuz the minimum would be 1 game per day

- anonymous

you are trying to minmize the number of days, by fitting the most games in one day

- anonymous

I don't think you're reading the whole question and given correctly.

- lgbasallote

what dp you mean @panlac01 ?

- lgbasallote

is there a different solution?

- lgbasallote

13C1 gives the same result though...

- lgbasallote

13 teams..one game per day...so 13C1 would make sense right?

- anonymous

no, there must be a total of 78 games

- anonymous

13 teams must play all the other teams

- lgbasallote

isn't that what 13C1 means?

- anonymous

with 13 teams, only 12 teams can play in one day

- anonymous

no 13 C 1 means the number of ways you can select 1 team from 13 teams

- anonymous

the question is, what is the minimum day that they can ALL play without any team playing more than 1 team a day

- lgbasallote

so what are you implying?

- anonymous

12 team playing on 1 day=6 games in total for the day

- lgbasallote

this was a question in a board exam back in '94 so it's meant to be tricky

- anonymous

in the first day, you are left with one team unable to play

- anonymous

so you need to move on to the second day to give that specific team who didn't play to play.

- lgbasallote

i really think 13C1 makes sense

- lgbasallote

in the case of (13C2)/6...why divide by 6? of all the numbers?

- anonymous

6 is the number of games played in 1 day by 12 teams

- lgbasallote

but what about for the case of 13 teams?

- anonymous

only 12 teams can play per day because they have to be grouped in teams of 2

- lgbasallote

i don't think that means the other team should be disregarded

- anonymous

its a 1v1 match, 2 teams per game

- anonymous

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

yes i get that. but im asking for the case of 13 teams. is that logic applicable in that case?

- lgbasallote

you used 13C2 and then divided by 6 (which is for 12 teams)

- anonymous

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

- anonymous

*groups of two teams out of 13 teams

- anonymous

so what is the answer with the formula being suggested?

- anonymous

ganesh is close

- anonymous

(13C2)/6
I really need to work on explaining things, hopefully openstudy will help me with that

- anonymous

don't worry bro, you got it from the first time. Illustration makes a better explanation sometimes.

- lgbasallote

so do you agree with pizzapi already @panlac01 ?

- PhoenixFire

@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.

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