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Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Does the topology matter? If I were to completely separate the two halves, would it make a difference?


.: [GEOM], [internet], [Topology].

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.: [ALG1], [internet], [Yohaku].

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If we are told that we have a quadrilateral inscribed in a circle with diameter 10, do we KNOW if the angle at B and the angle at D are \( 90^o \)? Because that sure would make it easier to find x.



.: [GEOM], [internet], [Wait. Really?].

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Marilyn Burns pointed out:




Well, does it?
Is there a pattern that always works?


.: [ALG1], [internet], [Number Theory].

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If the time is 10:10, what is the exact angle between the minute hand and hour hand?

How about 7:30?

How about 7:35?


.: [GEOM], [internet], [Puzzle].

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Consider a normal, everyday clock.

How many times per day do the hands make a straight angle? What are some of these times?

How many times per day do the hands make a right angle? What are some of these times?


.: [GEOM], [internet], [Notice, Wonder].

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Consider a normal, everyday clock face.

If the MINUTE hand is on 2, and the hour hand and minute hand make an acute angle, what time could it be?

If the MINUTE hand is on 8, and the hour hand and minute hand make an obtuse angle, what time could it be?


.: [MS Math], [internet], [Geometry Snacks].

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What's the angle between the red lines?


.: [GEOM], [internet], [New Understanding].

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Normally, I'm glad when the media talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.




What's the error?

Oh, and solve it if you want, too. It's not really that hard. Further questions:


  • Which blanks CANNOT have a prime number in them?

  • Which blanks COULD have certain prime numbers?

  • Which blanks essentially force this problem to be non-unique?


No snarky notes about the description of the Order of Operations!


.: [MS Math], [internet], [Puzzle].

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Does this graphic work?



Does this graph rely too much on the reader's knowledge of the city? Is that a problem?


.: [STATS], [internet], [Graphicacy].

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How did he pull this off?




Can you sketch this scene from the side?


.: [ALL], [internet], [Illusion].

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Here's the original Cafe Wall, after which the Cafe Wall Illusion was named.






What went wrong with this wall? What does every single bricklayer and tile-setter know as Rule #1, to avoid the Cafe Wall Illusion?


.: [ALL], [internet], [Illusion].