Suppose you have n ≥ 1 friends on facebook (where friendship is mutual.) Use the Pigeonhole Principle to show that at least two of all n + 1 of you have the same number of facebook friends within this group
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From a Course on the Introduction to Abstract Algebra 4. Use pigeonhole principle to show that ·Out of 15 people there are at least two that have their birthdays in the same month. ·Out of five points inside a square with the side length two there are at least two that are at most of distance of V2.
Suppose five points are randomly placed inside a square that measures 2 inches by 2 inches. Use the pigeonhole principle to prove that there must at least two points that are within V2 inches of each other. Suppose five points are randomly placed inside a square that measures 2 inches by 2 inches. Use the pigeonhole principle to prove that there must at least two points that are within V2 inches of each other.
Proposition PHP2. (The Pigeonhole Principle.) If n or more pigeons are distributed among k 0 pigeonholes, then at least one pigeonhole contains at least 1 pigeons. Proof. Suppose each pigeonhole contains at most 1-1 pigeons. Then, the total number of pigeons is at most k(P1-1) < k㈜ = n pigeons (because R1-1( , RI). Exercises. Prove: (a) If n objects are distributed among k>0 boxes, then at least one box contains at most L objects (b) Given t > 0...
Discrete math Pigeonhole principle/generalized pigeonhole principle question. Rental cars belong to one of twelve classications depending on size and type of car. Each car is also assigned one of six color categories. How many cars does a rental agency need to guarantee that there are at least two cars of the same classication and color?
Pigeonhole Principle 2. (10 pts) Using the Pigeonhole Principle, show that in every set of 100 integers, there exist two whose difference is a multiple of 37.
a be a real number . If a--a, prove that either a 0 or a 1. 8. (Pigeonhole Principle) Suppose we place m pigeons in n pigeonholes, where m and n are positive integers. If m > n, show that at least two pigeons must be placed in the same pigeonhole. [Hint (from Robert Lindahl of Morehead State University): For i 1, 2, . . . , n, let Xi denote the number of pigeons that are placed in the...
18. Prove the infinite pigeonhole principle, that is, let S be an infinite set, n E Zt. Prove that no matter how the elements of S are partitioned into n parts, at least one of the parts must be infinite 18. Prove the infinite pigeonhole principle, that is, let S be an infinite set, n E Zt. Prove that no matter how the elements of S are partitioned into n parts, at least one of the parts must be infinite
1 points According to the Generalized Pigeonhole Principle, what is the minimum number of cards that must be chosen from a standard deck to ensure that five have the same suit? 65 0 52 13 0 17
Given 11 different integers from 1 to 20. Prove that at least two of them are exactly 5 apart. pigeonhole principle.
There are 5 candidates running for student body president. There are 338 people who vote. Use the Pigeonhole Principle to determine the least number of votes a candidate could get while still winning the election?