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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
    I don't think there's any trick here. It's just a coincidence.2012-06-21
  • 2
    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.2012-06-21
  • 1
    It's also suspicious that none of those numbers are divisible by 3.2012-06-21
  • 15
    Have you seen [When multiplication mixes up digits](http://homepages.gac.edu/~wolfe/papers/pandigital/mathmag.pdf) ?2012-06-21
  • 0
    @PeterPhipps That clears a lot up :)2012-06-21
  • 3
    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 1000.2013-01-11

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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.)