Fold & Cut
What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?
What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?
Begin with a row of cups and end with all of the cups in a single stack.
Rules:
1. Count the number of cups in a stack. That stack must jump that number of
spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2
spaces; 3 cups have to move 3 spaces…
2. A cup or stack of cups cannot move into an empty space. They have to land
on another cup or stack of cups.
From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in the game of Liar’s Bingo, order seems to arise magically from something we first assume to be random or chaotic. In this case, we use the game of Liar’s Bingo to engage participants’ desire to find patterns, and supercharge that desire by demonstrating a magic trick that captivates attention by...
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In the television show Futurama, Professor Farnsworth and Amy decide to try out their newly finished “Mind-Switcher” invention on themselves. When they try to switch back, they discover a key flaw in the machine’s design: it will not allow the same pair of bodies to be used in the machine more than once. Is there a way to restore their minds back to their original bodies?
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A Mad Veterinarian has created three animal transmogrifying machines…
While grappling with the posed questions, players will explore a set of problems, figuring out how and if the machines can complete a given transformation. Connections can be made to invariants, abstract algebra, graph theory, and Leavitt path algebra.