Large Tic Tac Toe Tactics Number 3

Logic Level 3

You're playing a large Tic Tac Toe, with 5 in a row to win. It's your turn as $\color{#3D99F6} O$ .

What's the least number of moves you can make to win the game?

Assume the player $\color{#D61F06} X$ makes all the best possible moves to stay in the game (for as long as possible).

Screenshot made from the app RenjuWorld. No copyright infringement intended.

4 6 8 The victor of this game can't be decided yet 5 7

2 solutions

Kryon Krenoteve
Jun 16, 2015

Let's label the board like chess board. Let's label the columns from lower left corner as a,b,c, and so on, and rows from the lower left corner as 1,2,3 and so on. Now let us calculate the moves. 1) O's first play is c7, X must reply with b8. 2) Oe7, progressing towards a 5-row and attempt to create a double opportunity otherwise. Xf7, blocking the 5-row progress and developing its own 5-row diagonally. (Xd7 will only block its opponents progress.) 3) Oe6; a double opportunity. X can't reply with moves in g column or h column because it will lose in the race by one move. So, either block the horizontal 5-row, or block the vertical 5-row. Say, Xc6. 4) Oe4; Xe3 5) Oe8, win.

Notice that at move 2, X would have replied with Xe6, ruining the attempt of creating double opportunity. Even then, the least number of winning moves from this position remains the same.

I'm voting for this solution instead of the 4 moves.

Lego Haryanto - 5 years, 12 months ago

What follows after 2. Xe6 (blocking the double three-row)? What follows after 2. Xg6 (developing a line, just for the sake of lengthening the game)?

Ivan Koswara - 5 years, 12 months ago

I don't want to ruin your fun finding the answer out by yourself! I will just give three hints, they are the only techniques for playing this game: (1) Progressing and/or blocking the progress of opponent, (2) Creating a double opportunity and/or blocking opponent's attempt to make a double opportunity, (3) If possible, progress and block your opponent with one move. If not, then, if you fall behind your opponent, block him; else, only progress.

The move 2. Xg6 is not X's best move (the reason is explained in my solution of the problem), and thus does not satisfy the condition given in the question.

Kryon Krenoteve - 5 years, 12 months ago

I liked this problem very much, because rengo is one of my favorite game (after go, and hex). I carefully analyzed and found that at least 6 moves necessary, so I pressed the "6" and found out it is wrong, 5 is correct. I was excited - I get used to it, that this community makes every solution right eventually - WOW somebody found a solution with 5 steps - what can it be?

Then I read all the comments, looked right into, and found that the solution is not good and nobody else showed another working 5 step solution.

First, why is not good the solution made by Kryon Krenoteve?

He didn't consider F3 for X's second move.

After XF3 O has two options:

If O makes a double three with E6 (or any other solution where there is any point which is not a four-O-in-a-row threat), then X has the opportunity to make E3 and H3 as forcing moves, where O must answer before winning, which makes this (at least) a 7 moves solution.
So O must keep the pressure with fours always. O can make a win by making always fours: O's moves: F7, F8, C5, then either B4 or G9 depends on X's answer - which is a 6 moves solution.

Also F3 is a valid move, as it was stated: "Assume the player X makes all the best possible moves to stay in the game (for as long as possible)." And I showed above X stayed longer with F3 than with F7, which was considered in the solution.

Second I have to show, there is a 6 step solution.

What I found started with OF7, but Kyron's solution shows a 6 step solution, too. So there are 6 step solutions.

What do you think?

First Last - 5 years, 8 months ago

Umm I believe the answer is 4. The point is to get 3 in a row in a way that after the opponent is done his turn, there isn't an X on either end of the row. That way you put one O on either side of your row, in a way that there isn't an X right after. Now regardless of which side the opponent places the X you place an O at the other end of the row and you win.

So here's my solution.

Since X has no rows of 3 he isn't threatening O, so O can begin *attacking * .

First move, O is placed at E6 . X has to be placed at either C6 or G6 . Not doing so will let O make a row of four in the next turn and then a row of 5 after that.

Second move, O is placed at E4 . This is the game changer as there are now two free rows of 3 created from E6 to E4, and from D4 to F4. Now the opponent will try to block one of the rows if he doesn't want to forfeit. Let's just say he puts X at C4 . (other options include G4, E3, and E7)

Third move: place an O at E7 or E3 . You now have 4 in a row with no obstructions. Your opponent will block one side of the row, and then look down in shame.

Fourth Move: Win

Rishy Fishy - 5 years, 12 months ago

E6 as first O move is okay, but X will counter with G6 threatening with an open 3 in a row, ... O cannot not honor that, ... so second move of O E4 is fatal to O ...

Lego Haryanto - 5 years, 12 months ago

Oh, I see.

Rishy Fishy - 5 years, 12 months ago

Rishy Fishy
Jun 16, 2015

The point is to get 3 in a row in a way that after the opponent is done his turn, there isn't an X on either end of the row. That way you put one O on either side of your row, in a way that there isn't an X right after. Now regardless of which side the opponent places the X you place an O at the other end of the row and you win. So here's my solution. For sake of communication, I will label each column A, B, C, and so on from left to right. Each row is numbered 1, 2, 3, 4, from the top. For example the topmost X is at H2. First move, O is placed at E4. X has to be placed at either C4 or G4. Not doing so will let O make a row of four and then a row of 5. Second move, O is placed at E6. This is the game changer as there are now two free rows of 3 created from E4 to E6, and from D6 to F6. Now the opponent will try to block one of the rows if he doesn't want to forfeit. Let's just say he puts it at C6. (other options include G6, E7, and E4) Third move: place an O at E7 or E3. You now have 4 in a row with no obstructions. Your opponent will block one side of the row, and then look down in shame. Fourth Move: Win

Moderator note:

As pointed out by Ian, this solution is incorrect.

Large Tic Tac Toe Tactics Number 3

Screenshot made from the app RenjuWorld. No copyright infringement intended.

2 solutions

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