A direct solution without the assumption that the solution is a whole number
. . . (-/ .* % -/ .+)@:(2 2&$) 21 38 55 106 4 On Tue, Aug 14, 2018 at 1:37 PM, Jose Mario Quintana < jose.mario.quint...@gmail.com> wrote: > A brute-force approach assuming that the solution is a whole number, and I > am understanding the problem correctly, follows after a few blank lines... > > > > > > > > > > > > > > > > > > > > > > > > > > > ((0 = -/ .*@:(2 2$21 38 55 106 - ])"0) # ]) i.111 > 4 > > Checking, > > -/ .* (2 2$21 38 55 106 - 4) > 0 > > Indeed, 17 is a common factor. Actually, > > +./ 21 38 55 106 - 4 > 17 > > On Tue, Aug 14, 2018 at 2:07 AM, Skip Cave <s...@caveconsulting.com> > wrote: > >> Attempting to solve the following Quora problem: >> >> What number must be subtracted from 21, 38, 55, and 106 each so that the >> remainders (technically differences) are proportional? >> >> Subtract the integers 0-9 from all four integers in the problem. Then find >> the prime factors of each set of four integers. Finally look for columns >> that have common factors in all four results: >> >> ]b=.q: each 21 38 55 106-/a=.i.10 >> >> ┌────┬───────┬────────┬──────┬──────┬───────┬─────────┬───── >> ────┬─────┬─────┐ >> >> │3 7 │2 2 5 │19 │2 3 3 │17 │2 2 2 2│3 5 │2 7 │13 │2 2 3│ >> >> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼───── >> ────┼─────┼─────┤ >> >> │2 19│37 │2 2 3 3 │5 7 │2 17 │3 11 │2 2 2 2 2│31 │2 3 5│29 │ >> >> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼───── >> ────┼─────┼─────┤ >> >> │5 11│2 3 3 3│53 │2 2 13│3 17 │2 5 5 │7 7 │2 2 2 2 3│47 │2 23 │ >> >> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼───── >> ────┼─────┼─────┤ >> >> │2 53│3 5 7 │2 2 2 13│103 │2 3 17│101 │2 2 5 5 │3 3 11 │2 7 7│97 │ >> >> └────┴───────┴────────┴──────┴──────┴───────┴─────────┴───── >> ────┴─────┴─────┘ >> >> >> Now how can I write a J function that lists the column index in this array >> where all four sets of factors have at least one common factor? Spoiler - >> In the example, the 5th set (column index 4) has a common factor of 17. >> >> >> Skip >> >> >> Skip Cave >> Cave Consulting LLC >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm