Kindly see this trick question and help me know as to how it works:

A trick question

The answer is always 123456789, how does it works? Can someone help me out here?

  • 1
    $\begingroup$ I don't think there's any trick here. It's just a coincidence. $\endgroup$ – tomasz Jun 21 '12 at 13:33
  • 2
    $\begingroup$ It's not entirely coincidence: 246,913,578 = 2·123,456,789. So of course that's what you get if you multiply by 5 or divide by 2. But I find it surprising that that's what you get if you multiply by 7, and I think there's something else at work here. $\endgroup$ – MJD Jun 21 '12 at 13:39
  • 1
    $\begingroup$ It's also suspicious that none of those numbers are divisible by 3. $\endgroup$ – rschwieb Jun 21 '12 at 13:54
  • 15
    $\begingroup$ Have you seen When multiplication mixes up digits ? $\endgroup$ – Peter Phipps Jun 21 '12 at 14:11
  • 3
    $\begingroup$ What bothers me slightly is that some interesting numbers to multiply by that work are missing; why was the prime 17 (and 409 and 439) skipped but not 31? All the numbers less than 1000 which work are 1,2,4,5,7,8,10,11,13,16,17,20,22,25,26,31,35,40,50,55,65,70,80,85,100,110,115,125,130,155,160,170,175,200,205,209,215,220,250,260,265,305,310,350,355,400,409,418,425,427,439,500,550,650,700,800,818,850,875. As an aside, the next closest pandigital number starting with 2 is 213497865, with a mere 25 multipliers below 1000. $\endgroup$ – Mark S. Jan 11 '13 at 18:55

The numbers were specifically chosen so that all numerals are present. No coincidence, just the authors of the question trying to seem clever. (Not to say they didn't, but it's fairly easy to tell they set it up specifically to always work.)


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