All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Clever counting (Posted on 2015-08-07) Difficulty: 3 of 5
Some positive integers n have the property that the sum
[ n + reverse(n) ] consists entirely of odd (decimal) digits.
For instance, 36 + 63 = 99 and 409 + 904 = 1313.
We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either n or reverse(n).
There are 120 reversible numbers below one-thousand.

a. Evaluate how many reversible numbers are there
below 10k, k=2,3... up to 6 or 7 .

b. Analyze the results, aiming to find the relation (i.e. approximate function) between N(k) and k.

Source: Project Euler, modified.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re: part a computer solution wrong? | Comment 2 of 6 |
(In reply to part a computer solution by Charlie)

Correct me if I am wrong.
It is easy to see why odd-number-of-digits  number (except 3 digits) cannot be reversible. Just consider the middle digit meeting itself in the summation.- t needs a carry in....
By visual revision of your results:
100 20
1000 120
10000 720  
100000 720          , correct result if previous line correct
1000000 18720
10000000 68720   not acceptable,-zero 7 digit numbers

I do not see where I err. Please comment.


  Posted by Ady TZIDON on 2015-08-07 20:37:31
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information