That post did not travel well; trying again,
(-/ .* % -/ .+)@:(2 2&$)21 38 55 106 4 On Tue, Aug 14, 2018 at 5:30 PM, Jose Mario Quintana < [email protected]> wrote: > > A direct solution without the assumption that the solution is a whole > number > > . > > . > > . > > (-/ .* % -/ .+)@:(2 2&$) 21 38 55 106 4 > > > > On Tue, Aug 14, 2018 at 1:37 PM, Jose Mario Quintana < > [email protected]> 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 <[email protected]> >> 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
