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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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