+2864 We classify the types of equ-triangles starting with biggest to smallest.
The biggest is obviously the equ-triangle with a side length of 5, the smallest equ-triangle has a side length of 1.
Count the number of equ-triangles for each class. The first one has already been filled out for you.
| Side Length | Number of \(\Delta \) |
| 5 | 1 |
| 4 | ? |
| 3 | ? |
| 2 | ? |
| 1 | ? |
Now once you complete the table, just find the total up the number of equ-triangles for the table.
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+26393 Find the number of equilateral triangles in the grid (\(n=5\)).
\(a(n) = \Big\lfloor \dfrac{n(n+2)(2n+1)}{8} \Big \rfloor \)
Source: http://oeis.org/A002717
\(\begin{array}{|rcll|} \hline a(5) &=& \Big\lfloor \dfrac{5(5+2)(2*5+1)}{8} \Big\rfloor \\ &=& \Big\lfloor \dfrac{5*7*11}{8} \Big\rfloor \\ &=& \lfloor 48.125 \rfloor \\ &=& \mathbf{48} \\ \hline \end{array} \)
