A set of n = 32761 pigeons flies home, each to one of m= 15 large pigeonhole communities. What is the smalles 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 o 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 [J. See the earlier question regarding the floor function.
A set of n = 32761 pigeons flies home, each to one of m= 15 large pigeonhole communities. What is the smalles 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 o 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 [J. See the earlier question regarding the floor function.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:A set of n = 32761 pigeons flies home, each to one of m= 15 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
[J. See the earlier question regarding the floor function.
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