Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Question

Question

3. (5 marks) Prove that if the integers 1,2,3,...,65 are arranged in any order, then it is possible to look either left to ri

Prove that if the integers 1, 2, 3, . . . , 65 are arranged in any order, then it is possible to look either left to right or right to left through the list and find nine numbers that are in increasing or

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

decreasing i Result every sequence of n²ti distinct numbers contains a dubsequence of length of nts that is either increasing

- dimilarly I asrat it can be seen that d o ds must be greater than de which is contradiction . . : 7 subsequence of length n

Add a comment

Answer 2

Similar Homework Help Questions

There are many ways in which the nine digits (not including zero) can be arranged in a 3-by-3 square formation that represents a sum. For example, look at figure 1. There are also many ways to place t...

There are many ways in which the nine digits (not including zero) can be arranged in a 3-by-3 square formation that represents a sum. For example, look at figure 1. There are also many ways to place the digits in a 3-by-3 grid so that, in ascending order, they form a “rookwise” chain. In other words, moving from cell to cell without doubling back and without moving diagonally, we can trace through the numbers in order for example, figure 2....
1. (a) Choose 150 integers from this list {1, 2, ..., 298}, prove that there are...

1. (a) Choose 150 integers from this list {1, 2, ..., 298}, prove that there are two integers ni, n2 such that ni|n2 or n2|n1. (b) Let n1, 12, ... , 1201 be integers. Prove there exist three in- tegers ni, nj, nk E {n1, N2, ... , n201} such that 100 can divide the differences between any two of them.
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers...

1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...

Problem 13. (1 point) [3 Marks] Prove the following: Show that for any given 42 integers...

Problem 13. (1 point) [3 Marks] Prove the following: Show that for any given 42 integers there exist two of them whose sum, or else whose difference, is divisible by 80.
Let S be the set of distinct ordered triples comprised of the numbers 1, 2, 3, 4. To say that the...

Let S be the set of distinct ordered triples comprised of the numbers 1, 2, 3, 4. To say that the triple is distinct means that no number occurs twice in the triple. To say that the triple is ordered means that two triples in which the same numbers appear in a different order are considered to be different triples. Some of the elements of S are: 1,2,3), (1,2,4), (3,2,1), (3,2,4), (4,2,1), (4,3,2) We wish to list all of the...
1. Create List 2. Create Random integers 3. Search List Write a program that gets random...

1. Create List 2. Create Random integers 3. Search List Write a program that gets random integers and populates a list, then searches the list 1. Write a program that creates an empty list 2. Populate the list with 100 random integers 3. After creating the list, print the length of elements in the list 4. Select a range of numbers as 10 – 20 5. Find out the number of times ‘15’ appears in the list and print it...

Let n be an odd positive integer. Consider a list of n consecutive integers, not necessarily...

Let n be an odd positive integer. Consider a list of n consecutive integers, not necessarily starting with 1. Show that the average is the middle number (that is the number in the middle of the list when they are arranged in an increasing order). What is the average when n is an even positive integer instead. We learned that for the odd numbers, we would have to show why n-1/2(2k+n)+(k+n) all over n equals k+(n+1)/2.
Using Python3 Write a function that takes an array of integers and returns it in increasing...

Using Python3 Write a function that takes an array of integers and returns it in increasing order. There can be negative numbers, but they are treated as positive numbers. Example list= list=[-6,7,6,7,-9,1,0,-3,-2,1,4] Answer list= [0, 1, 1, -2, -3, 4, 6, -6, 7, 7, 3]
. 1. Prove by induction that for all integers n≥1, 4+8+12+...+4n = 2n^2+2n 2. A number...

. 1. Prove by induction that for all integers n≥1, 4+8+12+...+4n = 2n^2+2n 2. A number a is divisible by b if the remainder of dividing a by b is zero. For example 10 is divisible by 5 but 11 is not divisible by 5. Prove by induction that for all integers n≥1,11^n - 6 is divisible by 5. 3. Prove by induction that for all integers n ≥ 1, 3^n ≥ 2^n+n^2

Prove by Induction 24.) Prove that for all natural numbers n 2 5, (n+1)! 2n+3 b.)...

Prove by Induction 24.) Prove that for all natural numbers n 2 5, (n+1)! 2n+3 b.) Prove that for all integers n (Hint: First prove the following lemma: If n E Z, n2 6 then then proceed with your proof.

Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Homework Answers

Add Answer to:
Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Post as a guest

Earn Coins

There are many ways in which the nine digits (not including zero) can be arranged in a 3-by-3 square formation that represents a sum. For example, look at figure 1. There are also many ways to place t...

1. (a) Choose 150 integers from this list {1, 2, ..., 298}, prove that there are...

1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers...

Problem 13. (1 point) [3 Marks] Prove the following: Show that for any given 42 integers...

Let S be the set of distinct ordered triples comprised of the numbers 1, 2, 3, 4. To say that the...

1. Create List 2. Create Random integers 3. Search List Write a program that gets random...

Let n be an odd positive integer. Consider a list of n consecutive integers, not necessarily...

Using Python3 Write a function that takes an array of integers and returns it in increasing...

. 1. Prove by induction that for all integers n≥1, 4+8+12+...+4n = 2n^2+2n 2. A number...

Prove by Induction 24.) Prove that for all natural numbers n 2 5, (n+1)! 2n+3 b.)...

Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Homework Answers

Add Answer to: Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Post as a guest

Earn Coins

Add Answer to:
Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...