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 Get them up (Posted on 2014-10-01)
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.

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Unsatisfying computer proof | Comment 3 of 5 |
(In reply to Unsatisfying computer proof by Charlie)

Errata:  Oh, by the way, the number of possible configurations is 2^10, not 2^12.  And it is not true that all of the configurations achieved by the computer program have a number of upturned cards equal to 2 mod 4; many of them equal 0 mod 4.

 Posted by Steve Herman on 2014-10-02 10:22:56

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