Sunday Morning Math Games!
This Spring (2021) the SMMG will stand for Sunday Morning Math Games! Every other Sunday, we'll post a super fun math game and ask questions about it! If you have an answer to any of the questions we ask, you can either make a video of yourself explaining the answer and send it to us, or you can email us your answer at smmg@math.utexas.edu.
We will also have an SMMG Discord where, every other Sunday at noon, you will be able to ask volunteers questions about math and the games! If you want to join the SMMG Discord, or you can email us at smmg@math.utexas.edu with your first name and what school you go to and we will send you an invite link!
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SMMG – Game 1
Title: Two-pile Nim
Volunteer Office Hours: February 7, 2021, 12-2pm on Discord!
Intro Video/ Video Transcript
Game Link
Questions:
- Is it better to go first, second, or does it not matter?
- Does it matter how many objects are in the piles at the start?
- Is there a strategy you can follow such that you will never lose?
Hint Video--don't watch this until you've tried hard to answer the questions on your own--you'll be amazed what you can figure out without the hint!
Feel free to email me if you're still stumped and want another hint!
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SMMG – Game 2
Title: One-rook chess
Volunteer Office Hours: February 21, 2021, 12-2pm on Discord!
Intro Video/ Video Transcript
Questions:
- Are there starting squares from which there is a winning strategy for the player who goes first?
- Are there starting square from which there is a winning strategy for the player who goes second?
- Are there starting squares from which both players have a winning strategy?
- Are there starting squares from which neither player has a winning strategy?
- If you answered ``no" to any of these, why do you think it might be impossible?
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SMMG – Game 3
Title: Bridg-it
Volunteer Office Hours: March 7, 2021, 12-2pm on Discord!
Intro Video/ Video Transcript
Game Link
Questions:
- It is possible to tie?
- Does a winning strategy for player two exist?
Click here for hints!
- Imagine you are player one, and player two does have a winning strategy.
What can you do?
- If you assume that something is true, and use that to prove something that you already know is false (like 1=0), then you have shown
that the original thing you assumed is actually false.
This is called a proof by contradiction!
Check out the beginning of this video to learn more!
- (Challenge) What is an explicit winning strategy for player one?
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SMMG – Game 4
Title: Game-related puzzles!
Volunteer Office Hours: March 21, 2021, 12-2pm on Discord!
Click here for the list of puzzles!
We will discuss the puzzles at the office hours, so start thinking about them in the meantime!
If you get stuck then just
send an email to smmg@math.utexas.edu and you will receive a hint!
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SMMG – Game 5
Title: Cat and mouse!
Volunteer Office Hours: April 11, 2021, 12-2pm on Discord!
Intro video
/ Video Transcript
Questions:
- Try playing a few rounds of "cat and mouse" on each of the graphs
here.
- For each of them, does the cat or mouse always win?
- What features of a graph allow the mouse to win?
- What features of a graph allow the cat to win?
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SMMG – Game 6
Title: Dots and boxes!
Volunteer Office Hours: April 25, 2021, 12-2pm on Discord!
Intro video
/ Video Transcript
Game link!
Questions:
- Try playing a few rounds of dots and boxes on a 3-by-3 board.
(So smaller than in the video.)
- Does it seem to matter if you go first or second?
- Does there seem to be a winning strategy?
- Now try playing on a 4-by-4 board. Is there a strategy for this board?
- As you play, what kinds of configurations appear in the grid?
- Let's say the board looks like this at beginning of your turn:
Make a move to ensure that, no matter how your opponent plays, you will
win. Note that the number of moves already made is even, so you are player 1.
- Now let's say we're playing on a rectangular board, and it looks like this at the beginning of your turn:
Make a move to ensure that, no matter how your opponent plays, you will
win. Note that the number of moves already made is even, so you are player 1.
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