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CMC Puzzle Page
Throughout November and December, we'll include different puzzles in our newsletters and emails that you can solve with family, friends, or on your own. The puzzles and their solutions are below. Enjoy!
Puzzle 1: Octahedron Origami
Challenge: Make 12 of these origami units and assemble an octahedron like the ones shown on the table in the photo below!
CMC students build origami shapes, including an octahedron.
Solution: Check out this video for the solution. For an extra challenge: what other forms can you make using the Sonobe unit?
Puzzle 2: Funny Faces
Challenge: Three Math Circle students A, B, and C, who are all very wise, wake up from a nap (not in class). It turns out someone drew funny images on their faces while they were sleeping. They all start laughing as they look at each others’ faces. A little while later, one stops laughing. Why did they stop?
Solution: A assumes that his own face is clean. A is laughing at B and C, and he is thinking that B could be laughing at C and C could be laughing at B. However, C would figure out very quickly that their face is dirty, because there would be nobody else to laugh at, if A’s face is clean. But since B is laughing, this would mean C would stop laughing quickly. But C is laughing, which means A’s face is also dirty.
Puzzle 3: Bridge Crossing
Challenge:
A family of 4 is trying to cross a bridge.
The bridge is very dangerous and it is dark outside. The family has a single source of light, a flashlight, that needs to be carried at all times while crossing the bridge.
The different members of the family take different times to cross the bridge:
Abel takes 1 minute
Beth takes 2 minutes
Chelsea takes 4 minutes
David takes 8 minutes
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At most, two people can cross the bridge at a time, and they must have the flashlight with them. How can the whole family get across in the fastest way possible?
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Hint: this can be done in under 16 minutes!
Solution:
A and B go - 2 minutes
A goes back - 1 minute
C and D go together - 8 minutes
B goes back - 2 minutes
A and B go forward - 2 minutes