Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1–12 around a square, 3 numbers along each side of the square, that the numbers along at least one of the sides must add up to 20 or more. (b) How many friends must you have to guarantee at least 5 of them will have birthdays in the same month. Use the extended pigeonhole principle.
Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1–12 around a square, 3 numbers along each side of the square, that the numbers along at least one of the sides must add up to 20 or more. (b) How many friends must you have to guarantee at least 5 of them will have birthdays in the same month. Use the extended pigeonhole principle.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 8
(a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1–12
around a square, 3 numbers along each side of the square, that the numbers along at least
one of the sides must add up to 20 or more.
(b) How many friends must you have to guarantee at least 5 of them will have birthdays in
the same month. Use the extended pigeonhole principle.
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