Cool problem of the day! (1 Viewer)

Carrotsticks

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Excellent!

Consider the following diagram:



The pattern of circles is repeated infinitely and the triangle is equilateral.

What percentage of the whole triangle is covered by circles?
 

barbernator

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82.7% correct to 1dp?

this is wrong, i made a mistake
 
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barbernator

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would putting it in the form of a infinite product help? ive got no idea...
 

seanieg89

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Only nontrivial solns are the pairs (4,2), (2,4). Proof:



so we cannot have equality if x and y are not equal. Here I have assumed a commonly known limit expression for e (and the fact that this expression is increasing...an easy thing to check).
 

seanieg89

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Here's one I really liked in high school:

Find all solutions in positive integers to:

 

seanieg89

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All three unknowns are positive integers, that is the only restriction.
 

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