First a Few Questions

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Instructions - Tic-tac-toe

In this task you will play a version of the game Tic-tac-toe, your goal will be to find the best move given a starting position.

You will have the opportunity to get a bonus based on your performance. If your solution is correct you get a bonus of $1.

This version of the game Tic-tac-toe is played on a 6x6 board as displayed on the right. Please read the instructions carefully; there will be a quiz on the next step.
This version of the game Tic-tac-toe is played on a 10x10 board as displayed on the right. Please read the instructions carefully; there will be a quiz on the next step.
Two players, X and O, take turns marking the spaces on the board.
The player who succeeds in marking four neighboring spaces in a horizontal, vertical, or diagonal row wins the game.

In the image on the right, O won the game by marking four spaces vertically.
The player who succeeds in marking five neighboring spaces in a horizontal, vertical, or diagonal row wins the game.

In the image on the right, X won the game by marking five spaces vertically.
In this image X won by marking four spaces diagonally.
In this image X won by marking five spaces diagonally.

Please answer the following questions:

Who won?

Who won?

Who won?

X can win in one move. What is the move?

example: a1

O can win in one move. What is the move?

example: a1

Your task will be to find the winning move for X, such that X wins no matter what the O player does. Below is an example, please read it carefully.

Your task will be to determine whether a certain move that X makes will guarantee that X wins no matter what the O player does. Below is an example, please read it carefully.


When solving the problem, you will be able to use an interactive board (like the one below) to try different strategies.

When you click a square, an X or an O will appear (depending on who's turn it is).
You will need to make moves for both players when trying out strategies. Both players should play as best as they can and try to win, so you will need to try to make the best moves you can for both X and O.
It is X's turn to play. In this position, X can force a win in 2 turns. This means that X can win the game by placing 2 more marks, even when the O player plays as best as possible to win as well.

In this example, X can guarantee a win by playing b3. After that, no matter what move O will make, X will still win. For example, if O plays e3, X will play a3 and win, and if O plays a3, X will play e3 and win. Note that O cannot threaten X in any other position, so O will surely lose this game.

Use the board to verify that X will indeed ensure a win in two moves by playing b3. In the real task you will also be able to use an interactive board like this one. Please use it (and not pen and paper), because we want to see how people solve such problems.
Each X move you play will show the move number so you can easily count how many moves you've played.
It is X's turn to play. In this position, X can force a win in 2 turns. This means that X can win the game by placing 2 more marks, even when the O player plays as best as possible to win as well.

In this example, X can guarantee a win by playing b3 (square with thick boarder). After that, no matter what move O will make, X will still win. For example, if O plays e3, X will play a3 and win, and if O plays a3, X will play e3 and win. Note that O cannot threaten X in any other position, so O will surely lose this game.

Use the board to verify that X will indeed ensure a win in two moves by playing b3. In the real task you will also be able to use an interactive board like this one. Please use it (and not pen and paper), because we want to see how people solve such problems.
Each X move you play will show the move number so you can easily count how many moves you've played.
It is X's turn to play. In this position, X can force a win in 2 turns. This means that X can win the game by placing 2 more marks, even when the O player plays as best as psossible to win as well.

In this example, X can guarantee a win by playing b3. After that, no matter what move O will make, X will still win. For example, if O plays f3, X will play a3 and win, and if O plays a3, X will play f3 and win. Note that O cannot threaten X in any other position, so O will surely lose this game.

Use the board to verify that X will indeed ensure a win in two moves by playing b3. In the real task you will also be able to use an interactive board like this one. Please use it (and not pen and paper), because we want to see how people solve such problems.
Each X move you play will show the move number so you can easily count how many moves you've played.
It is X's turn to play. In this position, X can force a win in 2 turns. This means that X can win the game by placing 2 more marks, even when the O player plays as best as psossible to win as well.

In this example, X can guarantee a win by playing b3 (square with thick boarder). After that, no matter what move O will make, X will still win. For example, if O plays f3, X will play a3 and win, and if O plays a3, X will play f3 and win. Note that O cannot threaten X in any other position, so O will surely lose this game.

Use the board to verify that X will indeed ensure a win in two moves by playing b3. In the real task you will also be able to use an interactive board like this one. Please use it (and not pen and paper), because we want to see how people solve such problems.
Each X move you play will show the move number so you can easily count how many moves you've played.


First move to ensure a win for X is:
Is b3 a winning move for X:


Please briefly explain the strategy you used to solve the problem:

Find the winning move for O, such that O wins no matter what O does.
Note that to win, a player needs to have 4 consecutive marks (row, column or diagonal).
If you answer correctly, you will be asked to play the game against the computer, so try to remember the moves you make.
You have 10 minutes to solve the problem. A timer is shown below.


Is d6 a winning move for O?
If so, what is the next move X will need to make to ensure the win?
If not, what move can O make to block X?
Note that to win, a player needs to have 4 consecutive marks (row, column or diagonal).
After you submit your answer, you will be asked to explain your strategy and play the game against the computer, so try to remember the moves you make.
You have 10 minutes to solve the problem. A timer is shown below.


Good job, the first move you've chosen is correct! To see if the rest of your solution is correct, play the game against O.

This time, when you use the board, the computer will be making the moves for O. Click continue once you think you've won the game. You'll have 3 minutes to complete this stage.
You cannot undo a single move at this stage, but you can reset the game to start over.

Time left:

Time left:

In this position O can force a win in 4 turns. This means that O can win the game by placing 4 more marks, even when O plays to win as well.


Find O's winning strategy.

Use the board to try out different strategies. Each X move you play will show the move number so you can easily count how many moves you've played.
X can win the game in 5 moves no matter what O does. Is the first move to win the game d6 (square shown with thick black border)? Assume that both players try their best to win the game.

Use the board to try out different strategies. Each X move you play will show the move number so you can easily count how many moves you've played. Note that it is now the turn of the O player (after X played the square shown with the thick black border).
The board as been reset to its starting position as now you will be playing against the computer.
For your convenience, this is a list of the moves you played on the board when solving the problem (after the last time you reset the board):

You'll receive a bonus of $1 if you answer correctly and verify the solution on the board in the next screen



First move to win for O:
Is d6 a winning move for O?:

If you answered "yes", what is the next move that X should play (after f3) to enforce the win?
If you answered "no", what is the first move O should play to block X from winning?
Your answer:
:


How confident are you in your solution?
  • Not at all confident
  • Very confident

Below are three solutions - your proposed solution, followed by two solutions proposed by other participants.

Please examine all solutions (yours and the two proposed solutions) and vote for ALL solutions you think are correct

After the experiment you will be randomly matched with 3 other workers. If the majority of your group memebers vote on correct solutions, each of you will get an additional bonus of 10 cents.

Yours: ?

c6

f3

Please explain your voting:
Final Words

You completed this task. Thank you!

Please paste your code back in the amazon turk HIT. You have to paste the code in order to get paid.

This is your code:

code