:Between 500 and 1000, how many integers are multiples of 5?How do I read this?
page 68
Are 500 and 1000 excluded?
So that I would be finding how many integers are multiples of 5 starting at 501 and ending with 999?
The solution seems to start with 500 and end with 999 ------
[pause]
Reading (& re-reading) Chung's solution, it's apparent he means that 500 and 1000 are excluded, but his way of writing the solution is so different from the way I would write it that it looks like he's including 500 but excluding 1000.
His solution also seems to imply that you find the number of integers between 100 and 199 inclusive (i.e. how many integers starting with 100 and ending with 199) is to subtract 100 from 199.
Chung's book seems to be fantastically useful, but I'm wondering whether you need to be already scoring a 700 or so to understand it.
I will soldier on.
At the AoPS website are videos that go with the Intro to Counting & Probability textbook. Watch the first two videos for Chapter one and you'll get the idea on how to approach this problem.
ReplyDeletelgm -- THANK YOU!
ReplyDeleteActually, I learned how to go about this problem from the AofPS book on counting and probability. FABULOUS first chapter -- wonderful! I taught it to Chris as soon as I taught it to myself.
What confused me with Chung is that he seemed to be doing the problem wrong.
So far, Chung's book is extremely difficult to follow.
ReplyDeleteI think the problem sets are probably fantastic, though.
You should stop thinking that Chung's problem is well phrased. It isn't. A proper problem is not ambiguous in this way. "From x to y, inclusive" or "from x to y, exclusive", or "starting at x and up to by not including y" would all be better phrased.
ReplyDeleteDon't think he's doing the problem wrong. He's causing you to do the wrong problem. I would not use a book that is so ambiguous in wording.