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Clarification on problem 178
Posted: Mon Jan 21, 2008 7:57 am
by 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.
Re: Clarification on problem 178
Posted: Mon Jan 21, 2008 12:51 pm
by 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.
Re: Clarification on problem 178
Posted: Fri Jan 25, 2008 5:59 am
by Georg
You're right. I got the correct answer when not counting numbers containing the consecutive digits 09 or 90.
Problem 178
Posted: Tue Jun 17, 2008 6:58 pm
by relue
Does the problem include numbers start with 0 or not?
Re: Problem 178 clarification needed
Posted: Tue Jun 17, 2008 7:05 pm
by daniel.is.fischer
No, leading zeros are only allowed if explicitly mentioned.
Re: Problem 178
Posted: Mon Dec 13, 2010 9:17 am
by 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.
Re: Problem 178
Posted: Mon Dec 13, 2010 10:49 pm
by lg5293
I don't think that is correct. Your answer is too small, so you're probably missing some cases.
problem 178
Posted: Wed May 09, 2012 5:32 am
by 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?
Re: problem 178 - step numbers
Posted: Wed May 09, 2012 6:55 am
by TripleM
The only number that starts with a digit of 0 is 0. 0123456789 is not a number.
Re: problem 178
Posted: Wed Jan 14, 2015 10:41 pm
by cska
Can anybody confirm that 40692 is correct for the 10^20 and 1509203434 for the 10^30 limits? Thanks.
Re: problem 178
Posted: Thu Jan 15, 2015 3:30 am
by MHealy
Your result for 10^30 is over 10 times too big
Good luck.
Re: problem 178
Posted: Thu Jan 15, 2015 12:01 pm
by 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
Re: problem 178
Posted: Tue Jan 20, 2015 12:55 am
by angzhiping
cska wrote: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.
Re: problem 178
Posted: Tue Dec 01, 2020 5:52 pm
by 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.
Re: problem 178
Posted: Wed Dec 02, 2020 7:38 am
by DJohn
youth4ever wrote: Tue Dec 01, 2020 5:52 pm
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.