Batch 2 - Class 271 - Spatial Visualization - 3D tic-tac-toe
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Preclass Exercise:
- 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:
Attendance: Raghav, Aneesh, SiddhantJ, Rehaan, Kabir, Advay, Shikhar, Ayush, Vivaan, Rhea Chadha, Ryan Chadha, Rohan, Siddarth, Tarush, Yatharth, Mihir, Shubh, Vansh, Kushagra, Dhriti, Aarushi, Adyant
Class Notes: (Repeat from class 74)
- Visualize the figure for which the perspectives are shown below
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- 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
- 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?
3D Tic Tac Toe
- 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://pi.math.cornell.edu/~mec/2003-2004/graphtheory/tictactoe/tttanswer2.html
- Can you devise a simple set of winning moves?
- Answer: Explain using http://pi.math.cornell.edu/~mec/2003-2004/graphtheory/tictactoe/tttanswer3.html
- (Ryan's question) If there are three players playing 3D tic-tac-toe, can the game end in a draw
- Aarushi presented a solution through hit-and-trial, which came close
- Solution from the book: We already know how to make each layer a draw with a 2-player game. Now if Player A and B draw on the first layer, B and C on the second layer, and C and A on the third layer, then there can't be any winning lines across layers since no player is playing all three layers. QED.
Homework
- 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:
References: