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.
(In reply to part a computer solution
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:
100000 720 , correct result if previous line correct
10000000 68720 not acceptable,-zero 7 digit numbers
I do not see where I err. Please comment.