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Pigeonhole principle examples, Exercises of Elementary Mathematics

The application of the pigeonhole principle in problem-solving. The pigeonhole principle is a mathematical concept that states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. three problems that can be solved using the pigeonhole principle. The problems involve drawing socks randomly from a drawer, determining the number of students needed in a class to guarantee the same score on a final exam, and finding the minimum distance between two points in a unit square. solutions to the problems using the pigeonhole principle.

Typology: Exercises

2022/2023

Available from 07/13/2023

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| tea: When mit pigeons _pnter om_pigeon. holes (rn>0) se a must be foe hae haste) ete, than _ = | Problem 13 _ 1: Taschen amo rning , John draws socks | vandomly fyem his drawer: If there are i2 paits of SOCKS each palfa different colour; in the drawer _ sass how many " socks does John -haye to dyaw at most inorder “to get a_matched pait pas Answer : Pigeoholes- colors pigeons ~ SotKs cp oe Ca “ Here, (atl) Socks at least So, Ce contains ie ~*~ Socks for some a, f= 122) 12_ ProblecL 2: How many. Students must be in a class to guarantee that ‘at Least to student receive the same score on the final exam, if the exam is qraded on a scale from 0 +0 {00 points f (mavks are trteqers) Answer: Here pigeonhole principles. Pigeonholes : masks (from 0 to, too Pigeons : students