## Issue with some question for assignment: Pigeonhole Principle, equiv. relation, recurrance relation, etc

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
ffdude
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### Issue with some question for assignment: Pigeonhole Principle, equiv. relation, recurrance relation, etc

Hi i have few questions over here and need some expert/pro view with approaching the question. The proving one would be an issue to me as well. Hope people would be able to assist me here , because i am basically struggling with it :( thanks

http://imgur.com/IlpU8pE

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FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Issue with some question for assignment: Pigeonhole Principle, equiv. relation, recurrance relation, etc

Hi i have few questions over here and need some expert/pro view with approaching the question. The proving one would be an issue to me as well. Hope people would be able to assist me here , because i am basically struggling with it :( thanks

Write back showing what you've tried so far (so we can see what's going on) and we can try to help you get unstuck. Thanks!

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Issue with some question for assignment: Pigeonhole Principle, equiv. relation, recurrance relation, etc

Hi i have few questions over here and need some expert/pro view with approaching the question. The proving one would be an issue to me as well. Hope people would be able to assist me here , because i am basically struggling with it :( thanks

Q2(a) What is "the Aiken-Dueet ice-cream parlour question"? (Please type it out so we don't have to work with graphical text.)

Q2(b) If the numbers are m, m+a1, m+a2, ..., m+an, how many differences are there? (BTW: All differences will be of the form aj-ai, or else just aj if you're subtracting m from m+aj. The m's cancel out.) Given that the differences relate to remainders after division, where does this lead?

Q2(c) If she plays at least one game per day, what is her minimum games per week? If, by day "d", she has played gd games, her running total is g1, g2, ..., g77, because of seven days per week. If she played exactly 21 games in some stretch of days, then one of these values -- g1 + 21, g2 + 21, ..., g77 + 21 -- matches a value from the first list (because it's that day's total, plus 21, which matches another, later, day's total). Where does this lead?

Q3 Working from the definition of an equivalence relation, what have you done? Where are you stuck?