problem 178

[Georg]

Is 90 a step number? I think yes. But my answer to problem 178 was wrong. So I'm not sure whether I have to skip numbers containing the consecutive digits 09 or 90 to correct my answer.

[kotulek]

According to the definition, a number is a step number if the difference between each pair of consecutive digits equals one. Since the difference between 0 and 9 is 9 and not 1, 90 is not a step number.

[Georg]

You're right. I got the correct answer when not counting numbers containing the consecutive digits 09 or 90.

[relue]

Does the problem include numbers start with 0 or not?

[daniel.is.fischer]

No, leading zeros are only allowed if explicitly mentioned.

[naadv]

Hi,
Problem 178 (View Problem)
I'm stuck in this problem, and considering where my mistake is.
Meanwhile, can someone please verify me that the solution for the problem with the bound of 10^20 is 35899?

Thank you.

[lg5293]

I don't think that is correct. Your answer is too small, so you're probably missing some cases.

[tpgettys]

I am wondering if a pandigital number may begin with 0.
For example, in determining the number of 10 digit pandigital numbers, what is the answer?

problem 178 - step numbers
Consider the number 45656.
It can be seen that each pair of consecutive digits of 45656 has a difference of one.
A number for which every pair of consecutive digits has a difference of one is called a step number.
A pandigital number contains every decimal digit from 0 to 9 at least once.
How many pandigital step numbers less than 1040 are there?

[TripleM]

The only number that starts with a digit of 0 is 0. 0123456789 is not a number.

[cska]

Can anybody confirm that 40692 is correct for the 10^20 and 1509203434 for the 10^30 limits? Thanks.

[MHealy]

Your result for 10^30 is over 10 times too big

Good luck.

[cska]

Managed to solve this problem.. but it was at the edge of my abilities. I never thought I would be ever using 5-dimensional arrays

[angzhiping]

Managed to solve this problem.. but it was at the edge of my abilities. I never thought I would be ever using 5-dimensional arrays

You can most certainly find a way to use 3 dimensional arrays.

[youth4ever]

The only 10-digit pandigital step number is : 9876543210

For the case of 11-digit I found the following three numbers :
98765432101
89876543210
10123456789

Can you tell me please which is the 4-th pandigital step number of 11-digit length ?
Thanks.

[DJohn]

The only 10-digit pandigital step number is : 9876543210

For the case of 11-digit I found the following three numbers :
98765432101
89876543210
10123456789

Can you tell me please which is the 4-th pandigital step number of 11-digit length ?
Thanks.

Why do you think there is a fourth?
From your question, I am guessing that you've interpreted the problem as being about the number of 40 digit pandigital step numbers. It isn't - it's about the number of pandigital step numbers less than 10^40. That's not the same thing.