What Is The Smallest Nine Digit Number That Is Divisible By 11? No Digit Should Be Repeated

[oflakes]

What is the smallest nine digit number that is divisible by 11? No digit should be repeated!

[fiction-factory]

is 0 allowable as one of the digits?

[bhg481]

10000000010

[bhg481]

sorry, forgot the repeated.

[fiction-factory]

123457906?

[fiction-factory]

It's divisible by 11 - you get 11223446

[fiction-factory]

Found a smaller one
102347586

[fiction-factory]

I think the setter probably wasn't counting 0 as a digit and wanted the digits 1-9 to be used
So I suggest 123475869 may be the answer

[fiction-factory]

I hope I'm wrong but I have a feeling this may be one of those maths/science threads I put a good 20-30 minutes into but then never get the extra info I need or any other feedback

[Prudie]

You may be right FF, I started with 123456789 (assuming no zeros although that does seem illogical) and then did a bit of trial and all error and then gave up, there must be some rules that would limit the trials. Of course in the old days I would have written a simple program in Basic and run it on my BBCB :-)

[Tilly2]

I tried multiplying 11 by lots of numbers, until I got to a nine digit answer. Then, I gave up. :-)

[fiction-factory]

Any more thoughts on this, oflakes?

[JimF]

Also, I suppose that the OP means *exactly* divisible by 11 i.e. no remainder - every nine-digit number is divisible by 11...

[JimF]

So, on the assumption that:
- zero is not allowed
- no digit can be repeated (i.e. used more than once)

the answer is 123456795, which is exactly divisible by 11.

[JimF]

If zero is allowed, the answer is 102345683

[fiction-factory]

Yours includes 5 twice jimf

[fiction-factory]

and your one including a zero has two 3s

[JimF]

***! Back to the drawing board...

[elliemay1]

I can't see why 0 wouldn't be allowed, after all it is a digit

[fiction-factory]

I'm still going for 102347586
I'm assuming it can't start with a 0 as that would make it 8 digits really

[New Judge]

//no digit can be repeated (i.e. used more than once)//

//the answer is 123456795, which is exactly divisible by 11.//

Er...er...