How many people need to turn up to be sure of making at least one team?
So pigeonhole principle states when there are m objects to be divided into n sets then at least one contains r+1 objects. i.e m > nr
In this question the m objects should be 12 months in 5 people so 12>5*3?
How do you arrive at 49?
combinatorics discrete-mathematics pigeonhole-principle elementary-probability
asked Nov 27 at 10:39
Pumpkinpeach
628
add a comment |
So pigeonhole principle states when there are m objects to be divided into n sets then at least one contains r+1 objects. i.e m > nr
In this question the m objects should be 12 months in 5 people so 12>5*3?
How do you arrive at 49?
combinatorics discrete-mathematics pigeonhole-principle elementary-probability
asked Nov 27 at 10:39
Pumpkinpeach
628
add a comment |
So pigeonhole principle states when there are m objects to be divided into n sets then at least one contains r+1 objects. i.e m > nr
In this question the m objects should be 12 months in 5 people so 12>5*3?
How do you arrive at 49?
combinatorics discrete-mathematics pigeonhole-principle elementary-probability
asked Nov 27 at 10:39
Pumpkinpeach
628
So pigeonhole principle states when there are m objects to be divided into n sets then at least one contains r+1 objects. i.e m > nr
In this question the m objects should be 12 months in 5 people so 12>5*3?
How do you arrive at 49?
combinatorics discrete-mathematics pigeonhole-principle elementary-probability
combinatorics discrete-mathematics pigeonhole-principle elementary-probability
asked Nov 27 at 10:39
Pumpkinpeach
628
asked Nov 27 at 10:39
Pumpkinpeach
628
asked Nov 27 at 10:39
Pumpkinpeach
628
asked Nov 27 at 10:39
Pumpkinpeach
628
asked Nov 27 at 10:39
Pumpkinpeach
628
628
add a comment |
add a comment |
2 Answers
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The value we are trying to find in this problem is $m$, the number of people required to have at least one team of five people.
We want at least one team with $5$ players, so $r + 1 = 5 implies r = 4$.
The number of teams is the number of months, so $n = 12$.
Hence, according to your formula $m > 12 cdot 4 = 48$. The smallest such value is $m = 49$.
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
add a comment |
There are 12 possible months. Let's imagine "the worst" situation for finding team quickly: each new person has the most "unpopular" month of birth - so, ppl are distributed "uniformly" between month. How many ppl you need to have 4 of each type? 4*12=48. And then any new person (+1) will have 1 of 12 possible months of birth and 4+1=5 (team is made).
If ppl won't distribute uniformly, then you will need 48 or less (because if one group has 3, then another has 5). 4*12+1=49 is maximum, then.
answered Nov 27 at 10:51
Kelly Shepphard
2298
add a comment |
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2 Answers
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active
oldest
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2 Answers
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active
oldest
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oldest
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The value we are trying to find in this problem is $m$, the number of people required to have at least one team of five people.
We want at least one team with $5$ players, so $r + 1 = 5 implies r = 4$.
The number of teams is the number of months, so $n = 12$.
Hence, according to your formula $m > 12 cdot 4 = 48$. The smallest such value is $m = 49$.
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
add a comment |
The value we are trying to find in this problem is $m$, the number of people required to have at least one team of five people.
We want at least one team with $5$ players, so $r + 1 = 5 implies r = 4$.
The number of teams is the number of months, so $n = 12$.
Hence, according to your formula $m > 12 cdot 4 = 48$. The smallest such value is $m = 49$.
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
add a comment |
The value we are trying to find in this problem is $m$, the number of people required to have at least one team of five people.
We want at least one team with $5$ players, so $r + 1 = 5 implies r = 4$.
The number of teams is the number of months, so $n = 12$.
Hence, according to your formula $m > 12 cdot 4 = 48$. The smallest such value is $m = 49$.
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
The value we are trying to find in this problem is $m$, the number of people required to have at least one team of five people.
We want at least one team with $5$ players, so $r + 1 = 5 implies r = 4$.
The number of teams is the number of months, so $n = 12$.
Hence, according to your formula $m > 12 cdot 4 = 48$. The smallest such value is $m = 49$.
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
answered Nov 27 at 10:47
N. F. Taussig
43.5k93355
43.5k93355
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
add a comment |
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
How can number of teams be number of months?
– Pumpkinpeach
Nov 27 at 13:11
2
2
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
It says that the members of each team must be born in the same month of the year. Hence, the number of possible teams is equal to the number of months.
– N. F. Taussig
Nov 27 at 13:17
add a comment |
There are 12 possible months. Let's imagine "the worst" situation for finding team quickly: each new person has the most "unpopular" month of birth - so, ppl are distributed "uniformly" between month. How many ppl you need to have 4 of each type? 4*12=48. And then any new person (+1) will have 1 of 12 possible months of birth and 4+1=5 (team is made).
If ppl won't distribute uniformly, then you will need 48 or less (because if one group has 3, then another has 5). 4*12+1=49 is maximum, then.
answered Nov 27 at 10:51
Kelly Shepphard
2298
add a comment |
There are 12 possible months. Let's imagine "the worst" situation for finding team quickly: each new person has the most "unpopular" month of birth - so, ppl are distributed "uniformly" between month. How many ppl you need to have 4 of each type? 4*12=48. And then any new person (+1) will have 1 of 12 possible months of birth and 4+1=5 (team is made).
If ppl won't distribute uniformly, then you will need 48 or less (because if one group has 3, then another has 5). 4*12+1=49 is maximum, then.
answered Nov 27 at 10:51
Kelly Shepphard
2298
add a comment |
There are 12 possible months. Let's imagine "the worst" situation for finding team quickly: each new person has the most "unpopular" month of birth - so, ppl are distributed "uniformly" between month. How many ppl you need to have 4 of each type? 4*12=48. And then any new person (+1) will have 1 of 12 possible months of birth and 4+1=5 (team is made).
If ppl won't distribute uniformly, then you will need 48 or less (because if one group has 3, then another has 5). 4*12+1=49 is maximum, then.
answered Nov 27 at 10:51
Kelly Shepphard
2298
There are 12 possible months. Let's imagine "the worst" situation for finding team quickly: each new person has the most "unpopular" month of birth - so, ppl are distributed "uniformly" between month. How many ppl you need to have 4 of each type? 4*12=48. And then any new person (+1) will have 1 of 12 possible months of birth and 4+1=5 (team is made).
If ppl won't distribute uniformly, then you will need 48 or less (because if one group has 3, then another has 5). 4*12+1=49 is maximum, then.
answered Nov 27 at 10:51
Kelly Shepphard
2298
answered Nov 27 at 10:51
Kelly Shepphard
2298
answered Nov 27 at 10:51
Kelly Shepphard
2298
answered Nov 27 at 10:51
Kelly Shepphard
2298
2298
add a comment |
add a comment |
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