triangle puzzle
Answer is 30.
How?
ignore 225, it is to confuse, here we will use the triangles property that the sum of all the angles inside a triangle should be 180 degree.
so 75 + 75 + ? = 180
=> ? = 180 – 150
=> ? = 30
how many triangles do you see
How?
Let’s say the smallest triangle side is 1 cms, then
Number of triangles with side 1cms: 12(3+4+3+2 upward facing) + 12(downward facing)
Number of triangles with side 2cms: 6(3+2+1 upward facing) + 6(downward facing)
Number of triangles with side 3cms: 1(upward facing) + 1(downward facing)
how many triangles in this triangle
How?
Let’s say the smallest triangle side is 1 cms, then
Number of triangles with side 1cms: 10(1+2+3+4 upward facing) + 6(0+1+2+3 downward facing)
Number of triangles with side 2cms: 6(1+2+3 upward facing) + 1(downward facing)
Number of triangles with side 3cms: 3(upward facing)
Number of triangles with side 4cms: 1(upward facing)
how many triangles in this triangle
How?
Lets count…
By looking at it, first impression is … its very simple, But mind you! its not that easy !!!
So lets stick to the divide and conquer approach, we will divide this triangle into 3 equal triangles(triangle formed by connecting outer side to the center of the circle) and will count the number of triangles in each part and then by taking two or more parts together.
Number of triangles in one part: 4(non overlapping) + 3(overlapping) = 7 * 3 = 21
Number of triangles by taking two parts together: 8 = 8 * 3 = 24
Number of triangles by taking all three parts together: 2
