Online Course Discussion Forum

Areteem AIME Sprint Camp (NORMAL)

 
 
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Areteem AIME Sprint Camp (NORMAL)
by Ethan Sun - Monday, 22 January 2024, 6:36 PM
 

For problem 10... I'm kinda confused on how to do it effectively and smartly...

I can think of probably the only cases where you can have the right angles, like you have 3 right triangles and then an equilateral triangle OR you have four right triangles in it...

Is there a faster way? Or do I just "bash" this out using casework?

 
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Re: Areteem AIME Sprint Camp (NORMAL)
by John Lensmire - Tuesday, 23 January 2024, 10:47 AM
 

Unfortunately this is one of those problems that pretty much just needs to be worked through carefully with cases.

Of course the symmetry of a cube can come into play when counting the different cases, but also when thinking through whether you missed any cases.

I won't totally spoil the problem as it's good to think and worry about, but I will say there are not that many cases you actually have to consider.