Higher-Dimensional Tic-Tac-Toe | Infinite Series

Regular tic-tac-toe can get a bit boring -- if both players are playing optimally, it always ends in a draw. But what happens if you increase the width of the board? Or increase the dimension of the board? Or increase both?

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The standard game of tic-tac-toe is too easy. How can we, as mathematicians, play with the combinatorics of tic-tac-toe? There are (at least) three easy ways to modify the game of tic-tac-toe: increase the width of the board - like *this* 5x5 board - increase the dimension of the board - like *this* 3x3x3 board - or increase both, like this 4x4x4 board.


Challenge Winner of the How the Axiom of Choice Gives Sizeless Sets:
For Your Math

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow
Made by Kornhaber Brown (www.kornhaberbrown.com)

Resources:

Hales/Jewett paper: http://www.ams.org/journals/tran/1963...
Golomb/Hales paper: http://library.msri.org/books/Book42/...
https://www.youtube.com/watch?v=p1YzY...
http://www.austms.org.au/Gazette/2005...

Special Thanks: Benjamin Houston-Edwards and Nathan Kaplan

Mathologer Video:
https://www.youtube.com/watch?v=aDOP0...

Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco and Nicholas Rose who are supporting us on Patreon at the Lemma level!

See more here: https://www.youtube.com/watch?v=FwJZa-helig

Stand Up, Take A Seat, Reverse

This is a great review game for shapes, angles and more.

1) Draw the different shapes on the board.

2) Point to each shape and state its name.

3) Trainees duplicate the shape's name.

4) State the wrong name for some shapes.

5) When you say the wrong name trainees should stand up, sit down and turn around at their desks as fast as they can.

6) The side that does this the fastest understands.

7) Play until the class appears confident naming the shapes.

If you have some slower kids just select somebody from each side to play rock, paper, scissors for the point to avoid embarrassing a sluggish trainee that is last every time. This is a fantastic video game to obtain kids moving and to examine terms.

Draw the Teacher

This is a fun game particularly for more youthful students.

1) Draw two blank bodies on the board.

2) Have 2 students answer a question.

2) Trainees address and come to the board to draw a body part.

3) The group with the craziest looking instructor wins the video game.

4) I normally tell them which body part to draw.

If you want to extend the video game make the trainees draw things like earrings, facial hair, hats, shirt logo designs etc.

3D Tic-Tac-Toe

This is an enjoyable review game that includes everyone.

1) Draw 3 blank tic-tac-toe boards on the board.

2) Divide the class into two groups.

3) Choose two students and ask both a concern.

4) Trainees answer the questions then pertain to the board.

5) With the help of their team students choose where to put their X or O.

6) The team with the most lines at the end of the game wins.

If you wish to extend the video game include more tic-tac-toe boards.
Regular tic-tac-toe can get a bit boring -- if both players are playing optimally, it always ends in a draw. But what happens if you increase the width of the board? Or increase the dimension of the board? Or increase both?Support us on Patreon at https://www.patreon.com/pbsinfinitese...Tweet at us! @pbsinfiniteFacebook: facebook.com...