May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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5-18 Discrete Mathematical Structures
(2) Consider the subsets (1, 9), (2, 8), (3, 7), (4, 6), (5, 5).
These subsets are equivalent to pigeonholes. Hence, the number of pigeons (i.e., integers) to
make the sum 10 is 5 + 1 = 6.
Example 3 A bag contains orange, blue, and white socks. Find the minimum number of socks
that one needs to choose in order to get two pairs (four) of socks of the same colour.
Solution: Here, colours are pigeonholes and hence n = 3, and socks are pigeons and hence
k + 1 = 4
∴k = 3
Thus, nk + 1 = 3.3 + 1 = 10 socks (pigeons) are required so that 4 of them are of the same colour.
5.8.2 Extended Pigeonhole Principle
If m pigeonholes ...
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