Henry Ernest Dudeney/Modern Puzzles/208 - The Nine Squares Game/Solution

by : $208$

 * The Nine Squares Game

Solution
There are $2$ best plays:


 * $MN$, which is that suggested by
 * $HL$

Proof
Neither of $MN$ or $HL$ allow any boxes to be created immediately.

Playing:
 * $(A): \quad MN$

leaves the plays $HL$, $CD$ or $DH$ for the opponent.

Any other reply is a blunder which gives you $7$ boxes immediately, and the win.

After:
 * $(B): \quad HL$

you play $CD$ or $DH$, allowing his play of either $DH$ or $CD$, claiming $1$, and forcing a further play which gives you the remaining $8$ boxes.

After:
 * $(B): \quad CD$ or $DH$

you play $DH$ or $CD$, claiming $1$, then $HL$.

$B$'s next move gives you the rest.

Playing:
 * $(A): \quad HL$

leaves the plays $MN$, $CD$ or $DH$ for the opponent, and the same analysis is used, exchanging $HL$ and $MN$.