Talk:Henry Ernest Dudeney/Puzzles and Curious Problems/319 - The Ten Cards/Solution

$000X000$, $00X00X0X0$ and $0X00X000$ are shown to be winning positions for $A$.

It can be checked that the cases where the second/fourth card is flipped over can also be reduced to these three cases in turn 3.

Moreover, $A$ loses if the first/fifth card is flipped, because $B$ can force a position of:

$X0000X0000$

and whatever $A$ does, $B$ can transform it into one of the winning positions above (or more simply, $B$ can copy what $A$ does for the rest of the game in the other quadruplet.)

--RandomUndergrad (talk) 08:25, 10 April 2022 (UTC)