Puzzle-6 (CSAT-2011)

Find the number of triangles in the above diagram?

(A) 32 (B)23   (C)26   (D) 27 (E) 16

Solution follows here:

Sollution

First we start from each of the 3-corners.

From corner-1 : (1,2,3), (1,4,6), (1,7,10), (1,11,15)    --- 4

From corner-11 : (11,4,13), (11,2,14)                              --- 2

From corner-15 : (15,6,13), (15,3,12)                              --- 2

Now we  count all the smallest triangles excluding (1,2,3) which is already considered above:

 (2,4,5), (2,3,5), (3,5,6)                                                    ---3

 (4,7,8), (4,5,8), (5,8,9), (5,6,9), (6,9,10)                   ---5

 (8,12,13),(8,9,13),(9,13,14)                                          ---3

Now by considering “middle 3-points” of each side of the outer triangle, we get the following:

(2,7,9), (3,8,10), (12,5,14)                                 ---3

Now by considering “single middle point” of each side of the outer triangle, we get the following:

(4,6,13)                                                                     ---1

So the total number of triangles = 4+2+2+3+5+3+3+1 = 23

Answer (B)