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.)
re(2): part a computer solution wrong? | Comment 3 of 6 |
(In reply to re: part a computer solution wrong? by Ady TZIDON)

I find this lack of acceptance unacceptable.


Here are the first 40 7-digit numbers, their reverses and the sums:

2020909   9090202     11111111
2020929   9290202     11311131
2020949   9490202     11511151
2020969   9690202     11711171
2020989   9890202     11911191
2021909   9091202     11113111
2021929   9291202     11313131
2021949   9491202     11513151
2021969   9691202     11713171
2021989   9891202     11913191
2022909   9092202     11115111
2022929   9292202     11315131
2022949   9492202     11515151
2022969   9692202     11715171
2022989   9892202     11915191
2023909   9093202     11117111
2023929   9293202     11317131
2023949   9493202     11517151
2023969   9693202     11717171
2023989   9893202     11917191
2024909   9094202     11119111
2024929   9294202     11319131
2024949   9494202     11519151
2024969   9694202     11719171
2024989   9894202     11919191
2030809   9080302     11111111
2030829   9280302     11311131
2030849   9480302     11511151
2030869   9680302     11711171
2030889   9880302     11911191
2031809   9081302     11113111
2031829   9281302     11313131
2031849   9481302     11513151
2031869   9681302     11713171
2031889   9881302     11913191
2032809   9082302     11115111
2032829   9282302     11315131
2032849   9482302     11515151
2032869   9682302     11715171
2032889   9882302     11915191

  Posted by Charlie on 2015-08-07 22:27:09
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