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Digits on the rise


Best Answer jamieg, 12 October 2013 - 05:35 AM

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#1 bonanova

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Posted 12 October 2013 - 02:36 AM

What do 15 489 1256 and 24578 have in common?

They are positive integers whose digits are strictly increasing left to right.

 

How many of them are there?


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#2 Dariusray

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Posted 12 October 2013 - 02:55 AM

Please clarify if you mean

  1. how many positive increasing-digit integers in {the set of all possible digit combinations in the stated problem} or
  2. how many positive increasing-digit integers in {the set of all positive integers}

(I have a feeling it's the latter option...)


Edited by Dariusray, 12 October 2013 - 02:55 AM.

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#3 bonanova

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Posted 12 October 2013 - 03:24 AM

Correct. The latter: positive integers whose digits are strictly increasing left to right.


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#4 Dariusray

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Posted 12 October 2013 - 05:30 AM

Spoiler for Best method I could come up with--from brute force to pattern...


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#5 jamieg

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Posted 12 October 2013 - 05:35 AM   Best Answer

Spoiler for answer

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#6 bonanova

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Posted 12 October 2013 - 10:21 AM

There's an even simpler observation that immediately gives the correct answer.
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#7 jamieg

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Posted 13 October 2013 - 03:09 AM

There's an even simpler observation that immediately gives the correct answer.

 

I assumed there is,

Spoiler for given the fact that the answer is
, but I'm not sure right now why that is. 


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#8 bonanova

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Posted 13 October 2013 - 12:38 PM

There's an even simpler observation that immediately gives the correct answer.

 
I assumed there is,
Spoiler for given the fact that the answer is
, but I'm not sure right now why that is.

The power set (the set of all subsets) of a set of n objects has size 2n. For 9 digits, n=9. Then subtract off the empty set.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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