Consider all possible 1000 digit positive base 10 integers all of whose digits are odd. For how many of these integers, do each pair of adjacent digits differ precisely by 2 ?

Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

(In reply to Solution by Dej Mar)

Yes, the numbers match:

The output when the program is carried to the 999th generation:

 5656045390468656842148819323484516307248082115155808028498272240623648918690828
18643087906313012714407016128706090726645044425601375758806668771147590964845467
00533052207445366861644412435709437735140578029126233576901933762439681698504446

And the value Dej Mar gives:

?14*3^498
 5656045390468656842148819323484516307248082115155808028498272240623648918690828
18643087906313012714407016128706090726645044425601375758806668771147590964845467
00533052207445366861644412435709437735140578029126233576901933762439681698504446

Posted by Charlie on 2008-09-23 10:33:15