+0  
 
0
42
5
avatar

How many positive integers are there whose digits strictly increase from left to right?

 Apr 13, 2020
 #1
avatar
0

Which integers? 2-digit, 3-digit, 4-digit......etc????

 Apr 13, 2020
 #2
avatar+631 
0

The largest digit possible is 123456789. There is a limit.

AnExtremelyLongName  Apr 13, 2020
 #3
avatar+41 
0

I think it's 5-digit

MathsAreFun  Apr 13, 2020
 #4
avatar+41 
0

Oh yaaa youre right AnExtremelyLongName.

MathsAreFun  Apr 13, 2020
 #5
avatar+631 
+1

For example: 123 is the smallest 3 digit integer with digits strictly increasing left to right.

 

We list smallest numbers like cases in the example:

1 (does not count)

12

123

1234

12345

123456

1234567

12345678

123456789

 

Notice how for each of these cases. The number with \(n\) digits has \(10-n\) cases that fit the problem. Starting with the two digit numbers, the number of cases that fit the problem is 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = \(\boxed{36}\)

 

I'm not sure if this is correct, but it is my attempt on the problem.

AnExtremelyLongName  Apr 13, 2020

13 Online Users