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-   -   The Number | 26 Sep 2009 (http://www.go4expert.com/contests/the-number-26-sep-2009-t19563/)

 shabbir 26Sep2009 15:55

The Number | 26 Sep 2009

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

Re: The Number | 26 Sep 2009

It must be 9.

 nimesh 26Sep2009 19:30

Re: The Number | 26 Sep 2009

9 and 0 both

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

 shabbir 27Sep2009 11:12

Re: The Number | 26 Sep 2009

9

 xpi0t0s 27Sep2009 19:11

Re: The Number | 26 Sep 2009

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!).

 nimesh 27Sep2009 21:23

Re: The Number | 26 Sep 2009