RE: TIB: American High School Math Exam thingy...
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RE: TIB: American High School Math Exam thingy...
HI!
> 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 :)
I think I know where to begin. If I understood the task correctly, then
loga+logb+logc+logd+loge+logf=n and a,b,c,d,e,f and n are integers =>
log(a*b*c*d*e*f)=n => a*b*c*d*e*f=10^n
I could find 4 different combinations:
1,2,4,5,10,25=10^4
1,2,5,10,25,40=10^5
1,4,5,10,20,25=10^5
1,5,10,20,25,40=10^6
So the answer is 1/4
--
Joel Kuusk E-mail: joel@scorpion.aai.ee
joelk@ut.ee
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