MAT 344
Challenge Set 1
The following questions illustrate some interesting mathematical counting ideas which
will be the topic of future material in this course.
Each question can be answered by
simply writing down all of the possible cases step by step. Done correctly, this will lead
you to the general principle involved.
Try to prove your answer carefully.
1. Determine the number of positive integers less than or equal to 100 which are:
 odd (that is, not divisible by 2)
 not divisible by 2 or 5
 not divisible by 2, 5, or 11
2. Find the number of ways of giving 4 different colour pens to 2 people a) without any
restrictions b) so that each person gets at least one pen.
3. How many different addresses on Memory Lane can be constructed using the digits 0
through 9, assuming that no address can have more than 2 digits? ( Note: Think carefully
about what constitutes an address.)
4. Show that in any group of 13 people, at least two were born in the same month. ( O.K.,
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 Fall '06
 miller
 Set Theory, Natural number, Prime number, Finite set

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