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.
With the correction I get 18 sets.
ct=0;
c=combinator(25,6,'c');
for i =1:length(c)
p=prod(c(i,:)) ;
r=round(log(p)/log(6));
if 6^r==p
disp(c(i, :) )
disp([p r])
disp(' ')
ct =ct+1;
end
end
ct
1 2 3 4 6 9
1296 4
1 2 3 6 9 24
7776 5
1 2 3 6 12 18
7776 5
1 2 3 8 9 18
7776 5
1 2 4 6 9 18
7776 5
1 2 6 9 18 24
46656 6
1 3 4 6 9 12
7776 5
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
1 6 9 12 18 24
279936 7
2 3 4 9 12 18
46656 6
2 3 6 8 9 18
46656 6
2 3 9 12 18 24
279936 7
3 4 6 9 18 24
279936 7
3 6 8 9 12 18
279936 7
ct =
18
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Posted by Charlie
on 2023-05-04 15:45:58 |
corrected program and solution
