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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    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(3): part a computer solution wrong? | Comment 5 of 6 |
(In reply to re(2): part a computer solution wrong? by Charlie)

Thanks, Charlie.

I have spent about 3 hours trying to solve this puzzle analiytically and did not realize the difference between 5-digits and 7 digits  numbers (using zero is not the same  in  both cases!)


Now I face a peaceful weekend...

Added   (after reading    your 2nd comment):

Obviously, I knew nothing about the solution being available on the web. 







Edited on August 8, 2015, 2:00 am
  Posted by Ady TZIDON on 2015-08-08 01:52:13

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