"sorted numbers" have digits that, read from left to right,

[tripleL2009]

Numbers with two digits or more, in which the digits, reading from left to right, occur in strictly increasing order are known as sorted numbers. For example, 125, 14 and 239 are sorted numbers but 255, 74 and 198 are not.

Suppose that a completelist of sorted numbers is prepared and written in increasing order. The 100th number on this list is?

I feel very confused by this question?
Any one can help?
Thankx

 

[Denis]

Re: "sorted numbers" problem

HINT:
10-11 ; 12-19 = 8
20-22 ; 23-29 = 7
30-33 ; 34-39 = 6
So were now at 39 = 21st: kapish?

 

[pka]

It should be noted that in the literature 255 would be considered a sorted integer, whereas the integers in described in this question are known as strictly sorted.
There are only \(\displaystyle {10 \choose 3}=120\) three digit strictly sorted integers [012 is 3-digits].
Of those, there is only one beginning with 7; three beginning with 6; six beginning with 5; and ten beginning with 4. So what is the 100th strictly sorted integer?

 

[tripleL2009]

389
right?!

I still not surehow to use the idea of permination and combination.
How can i present to fellow student?
Cheers!

 

[pka]

What is it about my explanation that you think fellow students would not understand?
I did use combinations to solve the problem.
Any subset of three digits forms into a strictly sorted integer.
How many subsets of three digits are there? \(\displaystyle 10 \choose 3\).

How strictly sorted integers are there between 1000 and 100000?
Each of those would have five digits.
Well, how many subsets of five digits are there? \(\displaystyle 10 \choose 5\).
Note 04679 is one of those number formed from the subset {9,4,0,6,7} .

 

[Deleted member 4993]

Think about it this way:

You have sorted digits lined uo:

0 1 2 3 4 5 6 7 8 9

Now you will remove (choose) 7 numbers out of there.

How many ways can you do it ? - [sub:1psamtvx]10[/sub:1psamtvx]C[sub:1psamtvx]7[/sub:1psamtvx] = [sub:1psamtvx]10[/sub:1psamtvx]C[sub:1psamtvx]3[/sub:1psamtvx]

Pretty simple....

 

[tripleL2009]

Thankx for reply. I know how to explain the combination idea.

how to explain "Of those, there is only one beginning with 7; three beginning with 6; six beginning with 5; and ten beginning with 4. So what is the 100th strictly sorted integer?" :?:

 

[Deleted member 4993]

Thankx for reply. I know how to explain the combination idea.

how to explain "Of those, there is only one beginning with 7 only one sorted number 789

; three beginning with 6 <<< 678, 679 & 689

and so on...

; six beginning with 5; and ten beginning with 4. So what is the 100th strictly sorted integer?" :?: