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The first four stellations are represented below. How many dots are in the 20th stellation?

 May 18, 2019
 #1
avatar+4322 
+2

Hint: Try to figure out a pattern with the tessellations!

 May 18, 2019
edited by tertre  May 18, 2019
 #2
avatar+5788 
+4

\(\text{stellation $n$ has an $n \times n$ square of dots, and 4 identical triangular regions containing}\\ \dfrac{n(n-1)}{2} \text{ dots each}\\ dots_n = n^2 + 4\dfrac{n(n-1)}{2} = 3n^2 - 2n\\ \text{I leave you to plug 20 in}\)

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 May 18, 2019
edited by Rom  May 18, 2019
edited by Rom  May 18, 2019
edited by Rom  May 27, 2019
 #3
avatar
+2

400+4*190=1160

 May 19, 2019
 #4
avatar+4322 
+2

4(1+2+3+....19)=4*190=760. Add the 19*19 square, so 760+361=1121 dots in the twentieth stellations. 

 May 19, 2019

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