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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

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    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 ~

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    It must be 9.
     
  3. nimesh

    nimesh New Member

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    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

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  5. xpi0t0s

    xpi0t0s Mentor

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    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

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    nice answer XPT :)
     

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