12 of 13 Items .... Type: Strategy

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

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That's pretty much it: How many Geometry Theorems are needed to solve this extended problem?




.: [GEOM], [SolveMyMaths], [Strategy].

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Skimming the MTBoS Finds Interesting Things video from the Global Math department.


Which will be more likely to occur first
in a string of coin tosses, HTH or HTT?


This is the kind of question that becomes difficult because of assumptions made by the listener, assumptions that change the problem subtly and thus change the resulting expected probability.

The listener/reader here naturally changes this question to "Which group of three is more likely?", but that is not what he asked. We should refer back to the Monty Hall question.


.: [PROBABILTY], [Bob Lochel], [Strategy].

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Equilateral triangles tile the plane. Is it possible to select four intersection points that are the corners of a perfect square?


.: [GEOM], [James Tanton], [Strategy].

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Could this work? What might go wrong with this plan?




If you divided the pizza into EIGHT pieces, what would be your chances of having to pay?


.: [PROBABILTY], [T.R.Milne], [Strategy].

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What is the best way to find the perimeter of the rounded hexagonal shape, i.e., the length of the belt that would wrap around the six wheels?


Radius of each pulley is \(1\)


.: [GEOM], [T.R.Milne], [Strategy].

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Assuming that you get every question correct, and bet it all on the Daily Double, and the Daily Double happens at the most opportune time, and the Daily double is located in the absolute best place, how much can you win in the first round of Jeopardy?

And what is the best place for the Daily Double?

And the best time to get the Daily Double?



The prizes are twice as big when you get to the Double Jeopardy Round:




So let's keep this going ... how much can you theoretically win to this point?

In Final Jeopardy, you can bet it all ("Let it Ride", as gamblers say).




.: [LOGIC], [T.R.Milne], [Strategy].

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For what value(s) of \(x\) is \(x^2+x+1=2x\sqrt{x+1}\)?

There are many ways to solve this. Wolframalpha, DESMOS. or Geogebra will all give an answer but can you decipher the clues in the heading?

Look at the graphs for the equation in Wolfram. The curves appear to be tangent to each other at the point of intersection. Can you show this to be true? or not?


.: [PRE-CALC], [David Marain], [Strategy].

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.: [GEOM], [internet], [Strategy].

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\( tan(23^{\circ}) = \dfrac{274}{x} \)

What do you know about the size of \( x \)? Is it longer or shorter than 274?
What if the angle were \( -23^{\circ} \)?
What other values of \( x \) are possible?

Sketch the triangle and find the value of \( x \).


.: [GEOM], [T.R.Milne], [Strategy].

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\( sin(\theta) = \dfrac{274}{391} \)

What if the fraction were \( -\dfrac{274}{391} \)?

What do you know about the size of \( \theta \), compared to the common angles?

What other values of \( \theta \) are possible?

Sketch the triangle and find the value of \( \theta \).


.: [GEOM], [T.R.Milne], [Strategy].

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You are 1 of 999,999 people asked. You get to keep whatever 6-digit dollar amount you want as long as no one else chooses it. What do you choose?


.: [PROBABILTY], [T.R.Milne], [Strategy].

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What method would you use to answer this question?
Are there any other methods can you think of?




Can you generalise your method?
Suppose x = f(n,s) where for this question, n = 12, and s = 3.

Can you find a general form for f(n,3)?
How about f(12,s)?
How about f(n,s)?


.: [GEOM], [Nathan Day], [Strategy].