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# How many are there?

### #1

Posted 22 August 2014 - 02:52 AM

How many natural numbers are there, whose digits increase left to right? (this is from a book, so some of you might already know this one)

### #2

Posted 22 August 2014 - 05:06 AM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 22 August 2014 - 05:35 AM

bonanova,

I see no sense in you disallowing 12 or 123, because each of those numbers have strict increases

in their digits.

### #4

Posted 22 August 2014 - 07:39 AM

bonanova,

I see no sense in you disallowing 12 or 123, because each of those numbers have strict increases

in their digits.

He didn't disallow 12 or 24, he correctly disallowed 112, 224 etc. Without strcict increase, the asnwer would be infinite.

### #5

Posted 22 August 2014 - 01:35 PM

Barcallica.

the quoted pair of numbers in question are 12 and 123, not 12 and 24 as you stated.

And here is bonanova's pertinent quote so you can see to which am referring:

"Assuming strict increase and disallowing 1, 11, 12, 112, 122, 123, and numbers like that with repeats in them."

### #6

Posted 22 August 2014 - 03:04 PM

[disallowing ... a sequence such as this .... that has ... ] numbers like that with repeats in them

You didn't understand?

Seriously?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #7

Posted 22 August 2014 - 03:18 PM Best Answer

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #8

Posted 22 August 2014 - 03:32 PM

Spoiler for Second thoughts

That's a cool solution, but a small correction is required...

### #9

Posted 22 August 2014 - 03:36 PM

bonanova,

you communicated wrong. You included 12 and 123. Those are strictly numbers and not parts of sequences of numbers.

If you wanted numbers that began with those digits, then you need to put ellipses after those, as in:

"Assuming strict increase and disallowing 1..., 11..., 12..., 112..., 122..., 123..., and numbers like that with repeats in them."

Next time you can type out the word "sequence" or put in the ellipses so you don't pass on the wrong information.

**And no single digit numbers should be included, because they do not consist of numbers where the digits**

**are increasing from left to right.**

**Edited by Perhaps check it again, 22 August 2014 - 03:44 PM.**

### #10

Posted 22 August 2014 - 05:24 PM

Spoiler for Second thoughts

That's a cool solution, but a small correction is required...

Spoiler for correction

You're right. Good catch.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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