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7

1

$begingroup$

Two players are playing a game on a $4times4$ board. The players take turns adding either a white circle or a black circle into any empty square, so that the board makes a solvable masyu puzzle (with one or more possible solutions). The winner is the player who first makes the position uniquely solvable (i.e. a puzzle which only has one possible solution).

What move should the first player start with?

logical-deduction grid-deduction game

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asked 9 hours ago

jafejafe

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$endgroup$

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7

1

$begingroup$

Two players are playing a game on a $4times4$ board. The players take turns adding either a white circle or a black circle into any empty square, so that the board makes a solvable masyu puzzle (with one or more possible solutions). The winner is the player who first makes the position uniquely solvable (i.e. a puzzle which only has one possible solution).

What move should the first player start with?

logical-deduction grid-deduction game

share|improve this question

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

$endgroup$

add a comment | 

$begingroup$

Two players are playing a game on a $4times4$ board. The players take turns adding either a white circle or a black circle into any empty square, so that the board makes a solvable masyu puzzle (with one or more possible solutions). The winner is the player who first makes the position uniquely solvable (i.e. a puzzle which only has one possible solution).

What move should the first player start with?

logical-deduction grid-deduction game

share|improve this question

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

$endgroup$

share|improve this question

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

share|improve this question

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

asked 9 hours ago

jafejafe

33.2k55 gold badges9191 silver badges332332 bronze badges

1 Answer
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6

$begingroup$

Up to symmetries of the board, there aren't very many possible moves for the first player:

There are only five moves: black in A, black in B, black in F, white in B, and white in F.


Black in A doesn't work; the second player responds with black in K.

Black in B doesn't work; the second player responds with black in O.

Black in F doesn't work; the second player responds with black in P.

White in B doesn't work; the second player responds with black in K.

So the only possible answer is white in F.

Does this strategy work?

Let's check all possible responses to white in F (again, ignoring symmetry):

Black in A makes the puzzle unsolvable.

Black in B: respond with black in L.

Black in C makes the puzzle unsolvable.

Black in D: respond with black in J.

Black in G: respond with black in M.

Black in H: respond with black in M.

Black in K makes the puzzle unsolvable.

Black in L: respond with black in B.

Black in P: respond with white in B.


White in A makes the puzzle unsolvable.

White in B: respond with black in P.

White in C: respond with black in L.

White in D makes the puzzle unsolvable.

White in G: respond with black in N.

White in H: respond with black in J.

White in K: respond with white in L.

White in L: respond with white in K.

White in P makes the puzzle unsolvable.


So this first move does indeed work, and lets the first player win on their next turn.

share|improve this answer

answered 6 hours ago

Deusovi♦Deusovi

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6

$begingroup$

Up to symmetries of the board, there aren't very many possible moves for the first player:

There are only five moves: black in A, black in B, black in F, white in B, and white in F.


Black in A doesn't work; the second player responds with black in K.

Black in B doesn't work; the second player responds with black in O.

Black in F doesn't work; the second player responds with black in P.

White in B doesn't work; the second player responds with black in K.

So the only possible answer is white in F.

Does this strategy work?

Let's check all possible responses to white in F (again, ignoring symmetry):

Black in A makes the puzzle unsolvable.

Black in B: respond with black in L.

Black in C makes the puzzle unsolvable.

Black in D: respond with black in J.

Black in G: respond with black in M.

Black in H: respond with black in M.

Black in K makes the puzzle unsolvable.

Black in L: respond with black in B.

Black in P: respond with white in B.


White in A makes the puzzle unsolvable.

White in B: respond with black in P.

White in C: respond with black in L.

White in D makes the puzzle unsolvable.

White in G: respond with black in N.

White in H: respond with black in J.

White in K: respond with white in L.

White in L: respond with white in K.

White in P makes the puzzle unsolvable.


So this first move does indeed work, and lets the first player win on their next turn.

share|improve this answer

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges

$endgroup$

add a comment | 

6

$begingroup$

Up to symmetries of the board, there aren't very many possible moves for the first player:

There are only five moves: black in A, black in B, black in F, white in B, and white in F.


Black in A doesn't work; the second player responds with black in K.

Black in B doesn't work; the second player responds with black in O.

Black in F doesn't work; the second player responds with black in P.

White in B doesn't work; the second player responds with black in K.

So the only possible answer is white in F.

Does this strategy work?

Let's check all possible responses to white in F (again, ignoring symmetry):

Black in A makes the puzzle unsolvable.

Black in B: respond with black in L.

Black in C makes the puzzle unsolvable.

Black in D: respond with black in J.

Black in G: respond with black in M.

Black in H: respond with black in M.

Black in K makes the puzzle unsolvable.

Black in L: respond with black in B.

Black in P: respond with white in B.


White in A makes the puzzle unsolvable.

White in B: respond with black in P.

White in C: respond with black in L.

White in D makes the puzzle unsolvable.

White in G: respond with black in N.

White in H: respond with black in J.

White in K: respond with white in L.

White in L: respond with white in K.

White in P makes the puzzle unsolvable.


So this first move does indeed work, and lets the first player win on their next turn.

share|improve this answer

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges

$endgroup$

add a comment | 

$begingroup$

Up to symmetries of the board, there aren't very many possible moves for the first player:

There are only five moves: black in A, black in B, black in F, white in B, and white in F.


Black in A doesn't work; the second player responds with black in K.

Black in B doesn't work; the second player responds with black in O.

Black in F doesn't work; the second player responds with black in P.

White in B doesn't work; the second player responds with black in K.

So the only possible answer is white in F.

Does this strategy work?

Let's check all possible responses to white in F (again, ignoring symmetry):

Black in A makes the puzzle unsolvable.

Black in B: respond with black in L.

Black in C makes the puzzle unsolvable.

Black in D: respond with black in J.

Black in G: respond with black in M.

Black in H: respond with black in M.

Black in K makes the puzzle unsolvable.

Black in L: respond with black in B.

Black in P: respond with white in B.


White in A makes the puzzle unsolvable.

White in B: respond with black in P.

White in C: respond with black in L.

White in D makes the puzzle unsolvable.

White in G: respond with black in N.

White in H: respond with black in J.

White in K: respond with white in L.

White in L: respond with white in K.

White in P makes the puzzle unsolvable.


So this first move does indeed work, and lets the first player win on their next turn.

share|improve this answer

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges

$endgroup$

share|improve this answer

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges

answered 6 hours ago

Deusovi♦Deusovi

69.6k77 gold badges240240 silver badges304304 bronze badges