Recent questions tagged pigeonhole-principle

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1

CMI2019-B-3
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 in Combinatory by gatecse Boss (16.8k points) | 29 views

+2 votes

1 answer

2

UGCNET-June-2019-II-7
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 in Combinatory by Arjun Veteran (424k points) | 280 views

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0 answers

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 in Theory of Computation by Naveen Kumar 3 Boss (15.2k points) | 25 views

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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 in Combinatory by `JEET Boss (13.2k points) | 86 views

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 (5.7k points) | 119 views

0 votes

1 answer

6

Rosen-Pigeonhole 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 Active (5.1k points) | 138 views

0 votes

1 answer

7

Rosen-Pigeonhole 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 (5.1k points) | 71 views

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 (6.9k points) | 97 views

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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 in Combinatory by tusharp Loyal (7.3k points) | 27 views

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10

Combinatorics-Kenneth 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 (27.6k points) | 95 views

0 votes

2 answers

11

Number of ordered pairs

asked Jun 1, 2018 in Mathematical Logic by saumya mishra Junior (959 points) | 87 views

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 (317 points) | 164 views

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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 (317 points) | 76 views

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 (317 points) | 44 views

+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 (317 points) | 78 views

+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 (317 points) | 77 views

+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 (317 points) | 55 views

+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 (317 points) | 51 views

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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) | 169 views

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) | 169 views

+8 votes

5 answers

21

TIFR2018-A-6
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 (424k points) | 427 views

+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) | 1k views

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 (27.6k points) | 71 views

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 (27.6k points) | 67 views

+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) | 149 views

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) | 234 views

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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) | 58 views

+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 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

asked Aug 14, 2017 in Combinatory by gabbar Junior (517 points) | 1.4k views

+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) | 782 views

+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 (26.4k points) | 331 views

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