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Recent questions tagged pigeonholeprinciple
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CMI2019B3
There is a party of $n$ people. Each attendee has at most $r$ friends in the party. The friend circle of a person includes the person and all her friends. You are required to pick some people for a party game, with the restriction that at most one person is picked from each friend circle. Show that you can pick $\dfrac{n}{r^{2}+1}$ people for the game.
asked
Sep 13, 2019
in
Combinatory
by
gatecse
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17.4k
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40
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cmi2019
permutationandcombination
pigeonholeprinciple
+2
votes
1
answer
2
UGCNETJune2019II7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$
asked
Jul 2, 2019
in
Combinatory
by
Arjun
Veteran
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430k
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328
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ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
0
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0
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3
Peter Linz Edition 4 Exercise 4.3 Question 18 (Page No. 124)
Apply the pigeonhole argument directly to the language in $L=$ {$ww^R:w∈Σ^+$}.
asked
Apr 12, 2019
in
Theory of Computation
by
Naveen Kumar 3
Boss
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15.4k
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26
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peterlinz
theoryofcomputation
regularlanguages
pigeonholeprinciple
0
votes
0
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4
How to solve this question
If seven colors are used to paint 50 bicycles then which of the following statements need not be true? at least eight bicycles are of the same color at least seven bicycles are of the same color at least nine bicycles are of the same color at most eight bicycles are of the same color
asked
Jan 16, 2019
in
Combinatory
by
`JEET
Boss
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18.8k
points)

90
views
pigeonholeprinciple
0
votes
1
answer
5
Pigeon hole principle
A teacher gives a multiple choice quiz that has 5 questions, each with 4 possible answers: a, b, c,d What is the minimum number of students that must be in the class in order to guarantee that at least 4 answer sheets will be identical? how to do this problem
asked
Dec 21, 2018
in
Combinatory
by
Prince Sindhiya
Loyal
(
5.9k
points)

126
views
pigeonholeprinciple
0
votes
1
answer
6
RosenPigeonhole Principle
How many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds? what this question means?
asked
Oct 25, 2018
in
Combinatory
by
aditi19
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5.2k
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150
views
pigeonholeprinciple
permutationandcombination
counting
discretemathematics
0
votes
1
answer
7
RosenPigeonhole Principle
An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.
asked
Sep 24, 2018
in
Combinatory
by
aditi19
Active
(
5.2k
points)

80
views
pigeonholeprinciple
permutationandcombination
0
votes
2
answers
8
PigeonHole Principal
A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?
asked
Sep 3, 2018
in
Mathematical Logic
by
Na462
Loyal
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7k
points)

103
views
pigeonholeprinciple
permutationandcombination
counting
0
votes
0
answers
9
Rosen Pigeonhole principle
Not getting highlighted part how ceil N/K will be greater or equal to r?
asked
Jul 4, 2018
in
Combinatory
by
tusharp
Loyal
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7.6k
points)

29
views
pigeonholeprinciple
0
votes
0
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10
CombinatoricsKenneth Rosen (Ex 5.2 12)
How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and ($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5? My answer comes to be 26. Please confirm.
asked
Jun 23, 2018
in
Combinatory
by
Ayush Upadhyaya
Boss
(
29k
points)

96
views
pigeonholeprinciple
discretemathematics
0
votes
2
answers
11
Number of ordered pairs
asked
Jun 1, 2018
in
Mathematical Logic
by
saumya mishra
Junior
(
965
points)

94
views
pigeonholeprinciple
discretemathematics
0
votes
1
answer
12
Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
asked
May 29, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
323
points)

173
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
counting
+1
vote
1
answer
13
Combinatorics
Given m integers $a_1,a_2,....,a_m$ show that there exist integers $k,s$ with $0 \leq k < s \leq m$ such that $a_{k+1} + a_{k+2} + .....+a_s$ is divisible by $m$.
asked
May 29, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
323
points)

80
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
counting
0
votes
1
answer
14
Combinatorics
Show that of any $5$ points chosen within a square of length $2$ there are $2$ whose distance apart is atmost $\sqrt{2}$.
asked
May 28, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
323
points)

47
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
+1
vote
1
answer
15
Pigeonhole Principle (3)
Let $a_1,a_2,a_3,....a_{100}$ and $b_1,b_2,b_3,....b_{100}$ be any two permutations of the integers from $1$ to $100$. $a_1b_1,a_2b_2,a_3b_3,....,a_{100}b_{100}$ Prove that among the $100$ products given above there are two products whose difference is divisible by $100$.
asked
May 25, 2018
in
Combinatory
by
Sammohan Ganguly
(
323
points)

90
views
pigeonholeprinciple
permutationandcombination
+1
vote
1
answer
16
Pigeonhole Principle (2)
Suppose a graph $G$ has $6$ nodes. Prove that either $G$ or $G'$ must contain a triangle. ($G'$ is the complement of $G$.) Prove it using pigeonhole principle.
asked
May 25, 2018
in
Combinatory
by
Sammohan Ganguly
(
323
points)

80
views
pigeonholeprinciple
permutationandcombination
counting
+2
votes
1
answer
17
Pigeon hole (1)
Prove that out of hundred whole numbers one will always have $15$ of them such that the difference between any two of these $15$ numbers is divisible by $7$.
asked
May 25, 2018
in
Combinatory
by
Sammohan Ganguly
(
323
points)

57
views
pigeonholeprinciple
permutationandcombination
+1
vote
2
answers
18
Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.
asked
May 25, 2018
in
Combinatory
by
Sammohan Ganguly
(
323
points)

54
views
pigeonholeprinciple
permutationandcombination
0
votes
0
answers
19
Keneth Rosen
Show that among any n + 1 positive integers not exceeding 2n there must be an integer that divides one of the other integers.
asked
May 12, 2018
in
Mathematical Logic
by
ankit aingh
(
201
points)

188
views
pigeonholeprinciple
permutationandcombination
0
votes
2
answers
20
Kenneth Rosen Edition 6th Exercise 5.2 Example 9 (Page No. 350)
Suppose that a computer science laboratory has $15$ workstations and $10$ servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server ... of direct connections needed to achieve this goal? Please Explain in this question how pigeonhole principle is applied .
asked
Mar 6, 2018
in
Combinatory
by
Abhinavg
(
455
points)

172
views
kennethrosen
discretemathematics
counting
pigeonholeprinciple
+8
votes
5
answers
21
TIFR2018A6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
asked
Dec 10, 2017
in
Combinatory
by
Arjun
Veteran
(
430k
points)

464
views
tifr2018
pigeonholeprinciple
permutationandcombination
+1
vote
2
answers
22
Show that for every integer n there is a multiple of n that has only 0s and 1s in its decimal expansion.
asked
Oct 29, 2017
in
Mathematical Logic
by
hem chandra joshi
Active
(
4.1k
points)

1.1k
views
pigeonholeprinciple
0
votes
0
answers
23
Kenneth Rosen Ex 5.2
How many numbers must be selected from the set {1,2,3,4,5,6} to guarantee that at least one pair of these numbers add up to 7?
asked
Oct 24, 2017
in
Combinatory
by
Ayush Upadhyaya
Boss
(
29k
points)

73
views
kennethrosen
pigeonholeprinciple
0
votes
0
answers
24
Keneth Rosen ex 10 pg 350
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. proof is given in rosen but I am unable to get it. It would be good if someone could give a proof of it in a better way.
asked
Oct 24, 2017
in
Combinatory
by
Ayush Upadhyaya
Boss
(
29k
points)

69
views
kennethrosen
pigeonholeprinciple
+5
votes
2
answers
25
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
asked
Oct 11, 2017
in
Combinatory
by
Surya Dhanraj
Active
(
2.3k
points)

152
views
pigeonholeprinciple
discretemathematics
0
votes
0
answers
26
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.
asked
Aug 31, 2017
in
Combinatory
by
Harish Karnam
Active
(
1.3k
points)

246
views
#counting
pigeonholeprinciple
0
votes
0
answers
27
Mott Kandel Baker Ex. 1.7 Q. 23
The circumference of two concentric disks is divided into 200 sections each. For the outer disk, 100 of the sections are painted red and 100 are painted white. For the inner disk, the sections are painted red or white in an arbitrary manner ... that 100 or more of the sections of inner disk have their colors matched with the corresponding sections on the outer disk.
asked
Aug 18, 2017
in
Mathematical Logic
by
just_bhavana
Boss
(
12.1k
points)

59
views
pigeonholeprinciple
+1
vote
3
answers
28
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 blindfolded (without replacing any of it) to be assured of picking atleast one ball of each colour? a) 15 b) 16 c) 17 d)18
asked
Aug 14, 2017
in
Combinatory
by
gabbar
Junior
(
517
points)

1.4k
views
pigeonholeprinciple
discretemathematics
+15
votes
1
answer
29
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?
asked
Nov 7, 2016
in
Probability
by
Akriti sood
Boss
(
12.2k
points)

800
views
probability
pigeonholeprinciple
+4
votes
1
answer
30
MadeEasy Test Series: Combinatory  Pigeonhole Principle
A community of 5 members is to be formed out of 10 people. The names are written in chits of paper and put into 6 boxes. So how many chits will go into the same box? Anyone, please make me understand this question.
asked
Nov 1, 2016
in
Combinatory
by
vijaycs
Boss
(
26.5k
points)

338
views
madeeasytestseries
engineeringmathematics
discretemathematics
pigeonholeprinciple
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