# The Number | 26 Sep 2009

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

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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~ Б0ЯИ Τ0 С0δЭ ~

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It must be 9.

3. ### nimeshNew 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

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5. ### xpi0t0sMentor

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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!).

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