A set of n = 32761 pigeons flies home, each to one of m = 13 large pigeonhole communities. What is the smallest number of pigeons possible in the pigeonhole that contains the most number of pigeons? Give an exact integer. No credit for being close (that indicates a misunderstanding of the concept). Hint 1: In other words, determine the largest integer k such that n > km. Then, if you were distribute only km of then pigeons evenly among the m pigeonholes, there would be k pigeons in each hole with some (fewer than m) pigeons left over. After assigning any remaining pigeon(s), you are forced to have a pigeonhole with at least k + 1 pigeons, which is the smallest number of pigeons in the hole with the most pigeons. It may be helpful to draw a picture for small n and m as we did in class. m Hint 2: The largest integer k such that n > km is equivalently the largest integer k such that > k. Since an even distribution among the m holes is impossible in this case (i.e., will not be an integer), this k is precisely [J. See the earlier question regarding the floor function. m
A set of n = 32761 pigeons flies home, each to one of m = 13 large pigeonhole communities. What is the smallest number of pigeons possible in the pigeonhole that contains the most number of pigeons? Give an exact integer. No credit for being close (that indicates a misunderstanding of the concept). Hint 1: In other words, determine the largest integer k such that n > km. Then, if you were distribute only km of then pigeons evenly among the m pigeonholes, there would be k pigeons in each hole with some (fewer than m) pigeons left over. After assigning any remaining pigeon(s), you are forced to have a pigeonhole with at least k + 1 pigeons, which is the smallest number of pigeons in the hole with the most pigeons. It may be helpful to draw a picture for small n and m as we did in class. m Hint 2: The largest integer k such that n > km is equivalently the largest integer k such that > k. Since an even distribution among the m holes is impossible in this case (i.e., will not be an integer), this k is precisely [J. See the earlier question regarding the floor function. m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:A set of n = 32761 pigeons flies home, each to one of m = 13 large pigeonhole communities. What is the smallest
number of pigeons possible in the pigeonhole that contains the most number of pigeons?
Give an exact integer. No credit for being close (that indicates a misunderstanding of the concept).
Hint 1: In other words, determine the largest integer k such that n > km. Then, if you were distribute only km of
the n pigeons evenly among the m pigeonholes, there would be k pigeons in each hole with some (fewer than m)
pigeons left over. After assigning any remaining pigeon(s), you are forced to have a pigeonhole with at least k + 1
pigeons, which is the smallest number of pigeons in the hole with the most pigeons. It may be helpful to draw a
picture for small n and m as we did in class.
Hint 2: The largest integer k such that n > km is equivalently the largest integer k such that > k. Since an
even distribution among the m holes is impossible in this case (i.e., will not be an integer), this k is precisely
See the earlier question regarding the floor function.
m
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
