Choose 25 different positive integers no higher than fifty, such that none is a multiple of any of the others. What's the lowest total possible, and what's the set? (Note one such set would be 26 through 50 inclusive; however that set totals 950.)

I don't know if this is the smallest but I found

{8,12,14,17,18,19,20,21,22,23,25,26,27,29,30,31,33,35,37,39,41,43,45,47,49}

for a total of 711

My method was to start with 26 through 50 and work backwards, halving the largest possible values.  All the evens except 26 and 30 could be halved.  Then 24 and 16 could be halved again.

Posted by Jer on 2009-02-10 15:16:24