10 playing cards are placed face-down on a table, forming a circle.
Your are allowed to turn over simultaneously 4 cards that either:
a.)all 4 are consecutive,
or
b.) 2 are on the left and 2 on the right of any specific card chosen by you (i.e. out of 5 consecutive cards only the middle one remains unturned) .

By executing a final number of the above (a. or b.) procedures can you reach an "all face-up" state?

If yes, explain how.
Otherwise, prove why not.

(In reply to Satisfying analytical proof (spoiler) by Steve Herman)

That's a nice proof.  I got as far as thinking about a parity argument but got bogged down considering even/odd, 0's and 1's, modulus, and the addition of binary numbers.

Edited on October 2, 2014, 10:29 am

Posted by xdog on 2014-10-02 10:25:29