In how many ways can 6 different numbers be chosen from the first 25 positive integers such that the product of these numbers is a power of 6?
Note: This problem is adapted from a regional math competition for students up to grade 9 and calculators were not allowed.
ct=0;
c=combinator(25,6,'c');
for i =1:length(c)
p=prod(c(i,:)) ;
r=round(p^(1/6));
if r^6==p
disp(c(i, :) )
disp([p r])
ct =ct+1;
end
end
ct
finds these 10 combinations of numbers:
1 2 6 9 18 24
46656 6
1 3 4 9 18 24
46656 6
1 3 6 9 12 24
46656 6
1 3 6 9 16 18
46656 6
1 3 8 9 12 18
46656 6
1 4 6 9 12 18
46656 6
2 3 4 9 12 18
46656 6
2 3 6 8 9 18
46656 6
4 9 12 16 18 24
2985984 12
6 8 9 16 18 24
2985984 12
ct =
10
The line following each list of numbers contains the product and the number whose sixth power this is.
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Posted by Charlie
on 2023-05-03 16:26:21 |
computer solution (spoiler)
