## lgbasallote 3 years ago 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

1. Rohangrr

6 and a half days!

2. lgbasallote

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

3. Rohangrr

|dw:1348374494350:dw|

4. pizzapi

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

5. pizzapi

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

6. kulprit

18 DAYS

7. pizzapi

yep, 13C2

8. pizzapi

all possible ways to choose 2 team out of 13

9. lgbasallote

how are you all getting those?

10. lgbasallote

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

11. nphuongsun93

12 days. <-' I guess

12. lgbasallote

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

13. lgbasallote

13C1?

14. pizzapi

wait, so all the teams play 6 games each?

15. lgbasallote

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

16. pizzapi

13C2 divided by 6

17. pizzapi

since 6 games per day

18. lgbasallote

but how do you know 6 games per day?

19. lgbasallote

it wasn't given

20. panlac01

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

21. pizzapi

6 teams can play 1 game everyday

22. pizzapi

that's the maximum possible games

23. pizzapi

per day

24. lgbasallote

it's looking for minimum though

25. pizzapi

no, its 13 days, with 6 games per day

26. pizzapi

because a maximum of 6 games can be played per day

27. pizzapi

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

28. lgbasallote

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

29. pizzapi

total games=13C2

30. pizzapi

maximum games per day=6

31. 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

32. pizzapi

minimum days=total games/max games per day

33. pizzapi

@ganeshie8 each team can only play 1 game for day

34. pizzapi

*per

35. lgbasallote

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

36. ganeshie8

oops ! bad logic disregard that

37. pizzapi

no cuz the minimum would be 1 game per day

38. pizzapi

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

39. panlac01

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

40. lgbasallote

what dp you mean @panlac01 ?

41. lgbasallote

is there a different solution?

42. lgbasallote

13C1 gives the same result though...

43. lgbasallote

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

44. pizzapi

no, there must be a total of 78 games

45. pizzapi

13 teams must play all the other teams

46. lgbasallote

isn't that what 13C1 means?

47. panlac01

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

48. pizzapi

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

49. panlac01

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

50. lgbasallote

so what are you implying?

51. pizzapi

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

52. lgbasallote

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

53. panlac01

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

54. panlac01

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

55. lgbasallote

i really think 13C1 makes sense

56. lgbasallote

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

57. pizzapi

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

58. lgbasallote

but what about for the case of 13 teams?

59. pizzapi

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

60. lgbasallote

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

61. pizzapi

its a 1v1 match, 2 teams per game

62. pizzapi

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

63. lgbasallote

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

64. lgbasallote

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

65. pizzapi

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

66. pizzapi

*groups of two teams out of 13 teams

67. panlac01

so what is the answer with the formula being suggested?

68. panlac01

ganesh is close

69. pizzapi

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

70. panlac01

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

71. lgbasallote

so do you agree with pizzapi already @panlac01 ?

72. 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.