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# Digits on the rise

7 replies to this topic

### #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

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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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