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Recent questions tagged pigeonhole-principle

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3
Ace Academy Test Series Qn#7
A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same hash value? 3 4 10 64
A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same h...
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4
Ace Academy Test Series
A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same hash value? 3 4 10 64
A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same h...
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8
GATE ACADEMY TEST SERIES
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who co...
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10
GATE Overflow Test Series | Mock GATE | Test 1 | Question: 25
The minimum number of integers to be selected from the set $S = \{1, 2, \dots , 9\}$ so that the difference of at least two of the integers is guaranteed to be $5$ is ___________ $4$ $5$ $6$ $7$
The minimum number of integers to be selected from the set $S = \{1, 2, \dots , 9\}$ so that the difference of at least two of the integers is guaranteed to be $5$ is ___...
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13
Kenneth Rosen Edition 7 Exercise 6.2 Question 47 (Page No. 407)
An alternative proof of Theorem $3$ ... there is no increasing subsequence of length $n + 1,$ then there must be a decreasing subsequence of this length.
An alternative proof of Theorem $3$ based on the generalized pigeonhole principle is outlined in this exercise. The notation used is the same as that used in the proof in...
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16
Kenneth Rosen Edition 7 Exercise 6.2 Question 44 (Page No. 406)
There are $51$ houses on a street. Each house has an address between $1000\: \text{and}\: 1099,$ inclusive. Show that at least two houses have addresses that are consecutive integers.
There are $51$ houses on a street. Each house has an address between $1000\: \text{and}\: 1099,$ inclusive. Show that at least two houses have addresses that are consecut...
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20
Kenneth Rosen Edition 7 Exercise 6.2 Question 40 (Page No. 406)
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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