Real Mathematics: Numbers #8

Dotted Tic-Tac-Toe

Almost everyone knows how to play tic-tac-toe. Dotted tic-tac-toe is a multiplayer game to teach kids about number systems.

Rules:

  • Players throw a dice in turns.
  • Each square in the board has the capacity of 9 dots.
  • Players should put dots into one of the boxes as many as their dice shows.
  • While putting down dots, players must be careful not to exceed the capacity of the box. In such situations they have to put dots to another box that has capacity.
  • Whoever gets right to left, upside-down or diagonal three boxes will be the winner.

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Beauty of this game is although it is competitive, it requires help of your opponent.

An example:

In the first three rounds players get 5, 6 and 3 from the dice:

Fourth dice is 1 which gives second player a chance to complete a box.

In the next four rounds players get 5, 5, 6 and 4 which gives again second player to complete another box.

Game resolves in the next rounds as shown in the following:

Binary Tic-Tac-Toe

In this version of the game, use a coin instead of a dice.

Heads: 1

Tails: 0

  • Consider that a box can have either of the following: A head & tail (tail & head is the same) or a tail & tail.
  • A square can never had head & head, since 1+1=2 which is overload for the binary number system.
  • This means that every box is either 1+0=0+1=1 or 0+0=0.
  • So in this version of the game, x-o-x turns into 1-0-1. Right to left, upside-down or diagonal 1s or 0s wins the game.

IMG_5629

Once again, although the game is competitive, you’ll need your opponent’s help.

An Example:

First two coin tosses are both tails.

IMG_5630

Then four consecutive heads are tossed.

Game resolved after three consecutive tails.

M. Serkan Kalaycıoğlu

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