Question for Angela Fajardo

Probability Level pending

If the figure in the left is figure 1, the one in the middle is figure 2 and the one in the right is figure 3, find the total number of triangles in the 2016 th {2016}^{\text{th}} figure that follows this pattern.


The answer is 4064256.

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1 solution

Ashish Menon
Apr 18, 2016

In figure 1, there is 1 1 triangle.
In figure 2, there are 4 4 triangles.
In figure 3, there are 9 9 triangles.
(For clarification):-
In figure 4, there are 16 16 triangles.
In figure 5, there are 25 25 triangles.


So, we see that in the n th n^{\text{th}} figure, the total number of triangle is given by the formula n 2 n^2

So, in the 2016 th {2016}^{\text{th}} figure, there would be 2016 2 {2016}^2 triangles.
= 4064256 triangles. _\square

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