RE: TIB: American High School Math Exam thingy...


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RE: TIB: American High School Math Exam thingy...




yeah, my dad walked me over that last night... it's very funkily worded, but
you only have to understand that you're looking for log(abcdef) and then for
powers of 2 and 5 since those are the only primes that divide 10, and then
do a hand search.
thanks,
ak

:>> 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



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