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Recent questions tagged pigeonhole-principle

5 votes
2 answers
91
P and C doubt
How many number must be chosen from site {1 2 3 4 5 6 7 8 }such that at least two of them must have sum equal to 9? A.28 B.9 C.5 D.10
How many number must be chosen from site {1 2 3 4 5 6 7 8 }such that at least two of them must have sum equal to 9?A.28B.9C.5D.10
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0 votes
0 answers
92
Pigeonhole Principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games.
During a month with 30 days, a baseball team plays at least one game a day, but no morethan 45 games. Show that there must be a period of some number of consecutive days ...
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1 votes
3 answers
94
UPSC prelim test
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking atleast one ball of each colour? a) 15 b) 16 c) 17 d)18
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without repla...
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18 votes
1 answer
97
probabiltiy
5 integers randomly chosen from 1 to 2015. What is the probability that there is a pair of integers whose difference is a multiple of 4?
5 integers randomly chosen from 1 to 2015. What is the probability that there is a pair of integers whose difference is a multiple of 4?
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4 votes
2 answers
100
generalised pigeonhole principle
Show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. Attempt-:partition will be {(1,10),(2,9),(3,8)(4,7)(5,6)} now how to apply pigeonhole principle to find the answer?
Show that if seven integers are selected from the first10 positive integers, there must be at least two pairsof these integers with the sum 11.Attempt-:partition will be ...
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2 votes
1 answer
101
ISI2011-PCB-A-3b
The numbers $1, 2, \dots , 10$ are arranged in a circle in some order. Show that it is always possible to find three adjacent numbers whose sum is at least $17$, irrespective of the ordering.
The numbers $1, 2, \dots , 10$ are arranged in a circle in some order. Show that it is always possible to find three adjacent numbers whose sum is at least $17$, irrespec...
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1 votes
1 answer
102
ISI2012-PCB-A-1a
A group of $15$ boys plucked a total of $100$ apples. Prove that two of those boys plucked the same number of apples.
A group of $15$ boys plucked a total of $100$ apples. Prove that two of those boys plucked the same number of apples.
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3 votes
1 answer
103
ISI2015-PCB-A-2
Prove that in any sequence of $105$ integers, there will always be a subsequence of consecutive elements in the sequence, whose sum is divisible by $99$.
Prove that in any sequence of $105$ integers, there will always be a subsequence of consecutive elements in the sequence, whose sum is divisible by $99$.
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1 votes
1 answer
104
CMI2014-B-02
There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one student who is a member of more than half of the committees.
There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one stu...
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0 votes
0 answers
106
Pigeon Hole Principle
The least num of computers required to connect 8 computers to 4 printers to guarantee 4 comp can direct]ly access 4 printer is _____ 16 17 19 20 21
The least num of computers required to connect 8 computers to 4 printers to guarantee 4 comp can direct]ly access 4 printer is _____1617192021
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1 votes
1 answer
107
TIFR-2011-Maths-B-11
There exists a set $A \subset \left\{1, 2,....,100\right\}$ with $65$ elements, such that $65$ cannot be expressed as a sum of two elements in $A$.
There exists a set $A \subset \left\{1, 2,....,100\right\}$ with $65$ elements, such that $65$ cannot be expressed as a sum of two elements in $A$.
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2 votes
2 answers
109
pigeonhole
Prove that at a party where there are at least two people, there are two people who know the same number of other people there.
Prove that at a party where there are at least two people, there are two people who know the same number of other people there.
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0 votes
1 answer
110
pigeonhole
Show that there are at least six people in California (population: 37 million) with the same three initials who were born on the same day of the year (but not necessarily in the same year). Assume that everyone has three initials.
Show that there are at least six people in California (population: 37 million) with the same three initials who were born on the same day of the year (but not necessarily...
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1 votes
1 answer
111
pigeonhole
Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.
Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friends or four mutual enemies, and there are either...
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0 votes
1 answer
112
pigeonhole
Show that in a group of five people (where any two people are either friends or enemies), there are not necessarily three mutual friends or three mutual enemies.
Show that in a group of five people (where any two people are either friends or enemies), there are not necessarily three mutual friends or three mutual enemies.
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1 votes
1 answer
113
pigeonhole
Assume that in a group of six people, each pair of individuals consists of two friends or two enemies. Show that there are either three mutual friends or three mutual enemies in the group.
Assume that in a group of six people, each pair of individuals consists of two friends or two enemies. Show that there are either three mutual friends or three mutual ene...
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8 votes
1 answer
114
application of pigeonhole principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days...
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60 votes
9 answers
115
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such th...
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39 votes
6 answers
116
GATE CSE 2000 | Question: 1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is$3$$8$$9$$12$
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