perplexus.info :: Numbers : Clever counting

Clever counting (Posted on 2015-08-07)

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 10^k, 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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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

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