Batch 2 - Class 74 - 3D Tic Tac Toe (Spatial Visualization IV)

• Arrange six people in a pattern so that each of them can see exactly 4 other people. Note that a person in middle can block the view for what is beyond them.
• Answer:

• Visualize the figure for which the perspectives are shown below

• Answer: 

  

• Folding games: In each of the following, fold X onto Y, and then onto Z. Visualize your final shape and then mirror it about a vertical axis so that left and right positions are swapped. Then mentally rotate your final shape to match one of the possible answers
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• Answers: C A C
• F's Effect: How many times does the letter F appear in the sentence below

• Answer: 6
• Read the poster below quickly. Do you see anything wrong?

• Start with a normal tic-tac-toe game.
• How many different winning lines are there?
• If two optimal players are playing, what are the possible outcomes?
• Let us now visualize a 3D 3x3 tic tac toe. 
• How many different winning lines are there?
• What is a simple way to compute those?
• Can you visualize all the 49 winning lines?
• If two optimal players are playing, what are the possible outcomes?
• Answer: First person wins
• If two players are playing at random, what are the possible outcomes?
• Can this game ever end in a draw?
• Answer: No. Explain using http://www.math.cornell.edu/~mec/2003-2004/graphtheory/tictactoe/tttanswer2.html
• Can you devise a simple set of winning moves?
• Answer: Explain using http://www.math.cornell.edu/~mec/2003-2004/graphtheory/tictactoe/tttanswer3.html 

• Download the 3D Tic-tac-toe game on your phone/online (https://www.mathsisfun.com/games/foursight-3d-tic-tac-toe.html) - Note that this is a 4x4x4 tic tac toe game. Play and try to win. Competition next time!
• Arrange numbers 1-32 in a circle so that any two adjacent numbers sum to a square
• Answer: