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 hexagon
Again it is good to use symmetry here, we can brake this image into six small triangles each formed by one of the side of the hexagon and each of the triangle is divided in half by a line. we will count the number of triangles formed by each part and by taking two or more such parts together.
Number of triangles formed by one part: 3 so total 3*6 = 18.
Number of triangles formed by taking two adjacent parts together: 2*3(three such cases as for 3 cases it is zero) so total 6.
Number of triangles formed by taking three adjacent triangles: 2*6 ( for each case 2 triangles are possible) so total 12
Number of triangles formed by taking 4 or 5 parts together: 0
Number of triangles formed by taking all 6 parts together: 1
1 ? 12 11
6 7 14 13
8 5 10 15
4 2 9 3
Answer is 0 OR 16.
How?
Here, there is no special pattern except that they are continuous numbers which are jumbled up, so the missing number can either be 0 or 16.
5 13 8 # 11 11 # 6 ? 3
Answer is 9.
How?
Here, every middle element is the sum of the other two so answer should be 6+3 = 9.
how many triangles in this pentagon
How?
Lets count the number of triangles where side of the pentagon is one of the side of the triangle, for each one such side there are 6 triangles. but two of triangle has other side of the pentagon, those will be counted twice so we will count only one triangle for each side, so for five sides, total 5*5 = 25 such triangles.
Now, lets count the triangles where side of the pentagon is not the side of the triangle: there are 5+5 = 10 such triangles, this will be clear by the below diagram(5 green and 5 red triangles).
how many triangles in this pentagon answer
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
how many squares do you see here
As all the sides are either horizontal or vertical we can say squares diagonals should be parallel. Now to see if the diagonals are parallel or not, i have drawn the diagonals where its not clear if it is a square or rectangle in the image below.
You can see i have labelled few sides as x and y to help you.
So,
Number of squares with side x/2 = 4
Number of squares with side x = 4
Number of squares with side y = 3
Number of squares with side x+y = 6
Number of squares with side x+y = 0
Number of squares with side x+2y = 1
Number of squares with side 2x+2y = 1
IF 11*11 = 4, 12*12 = 9, Then 13*13 = ?
Given
11×11 = (1+1)*(1+1) = 4
12×12 = (1+2)*(1+2) = 9
13×13 = (1+3)*(1+3) = 16
IF 1 =2, 4 20, 6 =42, 9=90, Then 10 =?
Given 1 = 1^1 + 1,
4 = 4*4 + 4 = 20
6 = 6*6 + 6 = 42
9 = 9*9 + 9 = 90
10 = 10*10 + 10 = 110
IF 1 = 5, 2 = 11, 3 = 36, 4 = 150, Then 5 = ?
Given 1 = 5,
2 = 5*2 + (1) = 11
3 = 11*3 + (1 + 2) = 36
4 = 36*4 + (1 + 2 + 3) = 150
5 = 150*5 + (1 + 2 + 3 + 4) = 760
