Henry Ernest Dudeney/Modern Puzzles/203 - The Horse-Shoe Game/Solution

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Modern Puzzles by Henry Ernest Dudeney: $203$

The Horse-Shoe Game
This little game is an interesting companion to our "Noughts and Crosses".
There are two players.
One has two white counters, the other two black.
Playing alternately, each places a counter on a vacant point, where he leaves it.
When all are played, you slide only, and the player is beaten who is so blocked that he cannot move.
In the example, Black has just placed his lower counter.
Dudeney-Modern-Puzzles-203.png
White now slides his lower one to the centre, and wins.
Black should have played to the centre himself, and won.
Now, which player ought to win at this game?


Solution

Every game should end up as a draw.

The only way one player can win is through a blunder made by his opponent.


Proof


This theorem requires a proof.
In particular: Martin Gardner tells us that the analysis is in Edouard Lucas' Recreations Mathematiques.
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Sources

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