Re: TIB: American High School Math Exam thingy...
[Prev][Next][Index][Thread]
Re: TIB: American High School Math Exam thingy...
In a message dated 2/15/00 11:35:15 PM Eastern Standard Time,
ak@creativegeometry.com writes:
> here it is.
> Let I, M, and O ve distinct positive integers such that the product
> IMO=2001. What is the largest possible value of the sum I+M+O?
> I dunno, I just figured that it's best to have a very large number
> multiplied by a very small number so that the sum is maximum. Therefore I
> divided 2001 by 3, got 667, and my answer is 667+3+1=671 (e).
> The ones in the end are much more hardcore though. I'll copy one:
> 23. Professor Gamble buys a lottery ticket, which requires that he pick six
> different integers from 1 thru 46, inclusive. He chooses his #s s.t. the
sum
> of the base-10 logarithms of his 6 #s is an integer. It so happens that the
> integers on the winning ticket have the same property - the sum of the
> base-10 logarithms is an integer. What is the probability that Professor
> Gamble holds the winning ticket?
> 1/5; 1/4; 1/3; 1/2; 1
> anyone in for this? I didn't even know where to begin :)
> -ak
The answer to the second one is 1/2. As much as I enjoyed that one, I
preferred the coffee-milk problem. Everyone in a family has an 8 ounce cup
of coffee and milk (both in quantities > 0). One person fills his cup with
1/6 of the total amount of coffee used and 1/4 of the total milk used. How
many people are in the family? It's elegant mathematics. I could tell you
the answer, but it's more fun to watch you sweat : )