The Number | 26 Sep 2009

shabbir's Avatar, Join Date: Jul 2004
Go4Expert Founder
Find the number which when added to any other number does not change the sum of its digit to ultimately single digit.
SaswatPadhi's Avatar, Join Date: May 2009
~ Б0ЯИ Τ0 С0δЭ ~
It must be 9.
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
9 and 0 both

123 + 9 = 132 ...... 1+2+3 = 1+3+2 = 6
123 + 0 = 123 ...... 1+2+3 = 6
shabbir's Avatar, Join Date: Jul 2004
Go4Expert Founder
9
xpi0t0s's Avatar, Join Date: Aug 2004
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!).
nimesh, SaswatPadhi likes this
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
nice answer XPT