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The Number | 26 Sep 2009

Discussion in '$1 Daily Competition' started by shabbir, Sep 26, 2009.

  1. shabbir

    shabbir Administrator Staff Member

    Find the number which when added to any other number does not change the sum of its digit to ultimately single digit.
     
  2. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

    It must be 9.
     
  3. nimesh

    nimesh New Member

    9 and 0 both

    123 + 9 = 132 ...... 1+2+3 = 1+3+2 = 6
    123 + 0 = 123 ...... 1+2+3 = 6
     
  4. shabbir

    shabbir Administrator Staff Member

  5. xpi0t0s

    xpi0t0s Mentor

    Any number of 9s will do the trick, so 99 (+100-1), 999 (+1000-1) etc will all work
    198 will also work (200-2), as will 297 (300-3) and any "extension" (400-4, 500-5 etc, and 3000-3, 30000-3, etc).

    In short, the answer is any number of the form x*10^y-x.
    nimesh is also correct because y=0.
    x doesn't have to be less than 10; 125000-125 will also work for example (as will 1125: try it!).
     
  6. nimesh

    nimesh New Member

    nice answer XPT :)
     

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