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Kenneth Rosen Edition 7 Exercise 6.2 Question 36 (Page No. 406)
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A computer network consists of six computers. Each computer is directly connected to at least one of the other computers. Show that there are at least two computers in the network that are directly connected to the same number of other computers.
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Kenneth Rosen Edition 7 Exercise 6.2 Question 44 (Page No. 406)
There are $51$ houses on a street. Each house has an address between $1000\: \text{and}\: 1099,$ inclusive. Show that at least two houses have addresses that are consecutive integers.
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Kenneth Rosen Edition 7 Exercise 6.2 Question 43 (Page No. 406)
Show that if $f$ is a function from $S\: \text{to}\: T,$ where $S\: \text{and}\: T$ are nonempty finite sets and $m = \left \lceil \mid S \mid / \mid T \mid \right \rceil ,$ then there are at least $m$ elements of $S$ mapped to the same value ... $f (s_{1}) = f (s_{2}) =\dots = f (s_{m}).$
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Kenneth Rosen Edition 7 Exercise 6.2 Question 42 (Page No. 406)
Is the statement in question $41$ true if $24$ is replaced by $2?$ $23?$ $25?$ $30?$
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Kenneth Rosen Edition 7 Exercise 6.2 Question 41 (Page No. 406)
An arm wrestler is the champion for a period of $75$ hours. (Here, by an hour, we mean a period starting from an exact hour, such as $1\: \text{p.m.,}$ until the next hour.) The arm wrestler had at ... than $125$ total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly $24$ matches.
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