### Brain Teasers

# Wonder Number

Try to find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

### Answer

The number is: 1234567912345679 * 9 = 111111111

12345679 * 18 = 222222222

12345679 * 27 = 333333333

And so on...

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## Comments

The answer provided is incorrect. When nine, or any of its multiples, is multiplied by 123456789, the number 1111111101 is produced (or the number of the multiple of nine used), not 1111111111. If you do not have the correct answer for a teaser, you should not submit it! This is...just foolish!

Oh crap! I misread the answer! My mistake, I thought it said 123456789, I did not see that the 8 was omitted. My deepest apologies. I was the foolish one, I am really sleepy though, my eyes were probably crossed when I looked at it!

No harm done mozven, appology accepted

Doesn't hold true after 81.

majd, buddy, you lost me two points. When I edited this one I said we should reject it because the answer is invalid for values over 81. Looks like I was in the minority. Those two points are really going to kill me. ...ah, but that's life I guess. I'll try not to hold it against you.

i also found your answer incorrect, when i tried it was 1111111101 and then 2222222202 etc... or have i dont the calculation wrong? i'm sorry, im ever so confused :-$

Easy enough: I just divided 111111111 by 9 = 12345679.

I first came across this puzzle in the biography of Lewis Carroll (AKA Charles Dodgson) lecturer in Mathematics at Oxford and author of Alice in Wonderland. He asks a child if he was good at multiplying and which numeral he had trouble writing. The child replied '5' so Charles got him to multiply 12345679 by 45. It's a good party trick.

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Yeah, I don't like that the teaser states that it will work for ANY multiple of 9. The teaser is also verbally atrocious, in my opinion. However, it is in fact pretty neat. Here's my edit:

"Try to find a whole number n that, for any single-digit whole number x, the product of n * 9 * x is a number all of whose digits are equal to x."

Call me too proper, but it's just so much easier to understand in my opinion. I actually misunderstood the question and thought the answer was going to be 101010101... etc., as long as you want it to be.

"Try to find a whole number n that, for any single-digit whole number x, the product of n * 9 * x is a number all of whose digits are equal to x."

Call me too proper, but it's just so much easier to understand in my opinion. I actually misunderstood the question and thought the answer was going to be 101010101... etc., as long as you want it to be.

Also, just realized that there are infinite answers to this teaser.

12345679, or

12345679012345679, or

12345679012345679012345679,

etc.

12345679, or

12345679012345679, or

12345679012345679012345679,

etc.

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