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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged pigeonholeprinciple
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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
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Combinatory
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Arjun
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ugcnetjune2019ii
permutationandcombination
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Peter Linz Edition 4 Exercise 4.3 Question 18 (Page No. 124)
Apply the pigeonhole argument directly to the language in $L=$ {$ww^R:w∈Σ^+$}.
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Apr 12
in
Theory of Computation
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Naveen Kumar 3
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peterlinz
theoryofcomputation
regularlanguages
pigeonholeprinciple
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How to do this question.
Disk request come into disk driver for cylinders 5, 17, 60, 125, 28, 170, 8, 32. Total moves using SCAN algorithm when disk head is currently positioned at 35 and moving toward higher cylinder number________.(Disk system has 200 cylinders (0  199)
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Jan 21
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Operating System
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`JEET
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53
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opea
pigeonholeprinciple
diskscheduling
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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
in
Combinatory
by
`JEET
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3.5k
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75
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pigeonholeprinciple
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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
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Combinatory
by
Prince Sindhiya
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5.4k
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100
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pigeonholeprinciple
0
votes
1
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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
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Combinatory
by
aditi19
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4k
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110
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pigeonholeprinciple
permutationandcombination
counting
discretemathematics
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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.
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Sep 24, 2018
in
Combinatory
by
aditi19
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4k
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65
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pigeonholeprinciple
permutationandcombination
0
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2
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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
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6.6k
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83
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pigeonholeprinciple
permutationandcombination
counting
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9
Rosen Pigeonhole principle
Not getting highlighted part how ceil N/K will be greater or equal to r?
asked
Jul 4, 2018
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Combinatory
by
tusharp
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6.7k
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25
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pigeonholeprinciple
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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
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25.4k
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83
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pigeonholeprinciple
discretemathematics
0
votes
1
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11
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
(
311
points)

153
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
counting
0
votes
1
answer
12
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
(
311
points)

72
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
counting
0
votes
1
answer
13
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
(
311
points)

42
views
engineeringmathematics
discretemathematics
permutationandcombination
pigeonholeprinciple
+1
vote
1
answer
14
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
(
311
points)

76
views
pigeonholeprinciple
permutationandcombination
+1
vote
1
answer
15
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
(
311
points)

69
views
pigeonholeprinciple
permutationandcombination
counting
+2
votes
1
answer
16
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
(
311
points)

51
views
pigeonholeprinciple
permutationandcombination
+1
vote
1
answer
17
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
(
311
points)

44
views
pigeonholeprinciple
permutationandcombination
0
votes
0
answers
18
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)

144
views
pigeonholeprinciple
permutationandcombination
0
votes
2
answers
19
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
(
449
points)

159
views
kennethrosen
discretemathematics
counting
pigeonholeprinciple
+7
votes
4
answers
20
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
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416k
points)

349
views
tifr2018
pigeonholeprinciple
permutationandcombination
+1
vote
2
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21
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
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(
4k
points)

922
views
pigeonholeprinciple
0
votes
0
answers
22
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
(
25.4k
points)

70
views
kennethrosen
pigeonholeprinciple
0
votes
0
answers
23
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
(
25.4k
points)

65
views
kennethrosen
pigeonholeprinciple
0
votes
0
answers
24
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
(
1.2k
points)

219
views
#counting
pigeonholeprinciple
0
votes
0
answers
25
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
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(
12k
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56
views
pigeonholeprinciple
+1
vote
3
answers
26
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
27
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
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12.1k
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762
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probability
pigeonholeprinciple
+4
votes
1
answer
28
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
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26.2k
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320
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madeeasytestseries
engineeringmathematics
discretemathematics
pigeonholeprinciple
0
votes
0
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29
Kenneth Rosen Edition 6th Exercise 5.2 Example 4 (Page No. 348)
show that for evry n there is a multiple of n such that its decimal expansion has only 0's and 1's.
asked
Oct 14, 2016
in
Combinatory
by
Aayushi Aggarwal
(
161
points)

165
views
pigeonholeprinciple
kennethrosen
discretemathematics
+3
votes
2
answers
30
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?
asked
Aug 25, 2016
in
Combinatory
by
sourav.
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15.9k
points)

758
views
pigeonholeprinciple
permutationandcombination
counting
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