## 1.) How many triangles are in this picture ?

See Answer### There are a total of 20 triangles.

**How?**

Lets count…

Assuming smallest side of a triangle is 1 cms.

Number of triangles with side 1 cms: 12(1 + 5 + 5 +1)

Number of triangles with side 2 cms: 6(1 + 2(triangles facing upward), 1+2(triangles facing downward))

Number of triangles with side 3 cms: 2(1 triangle facing upward and 1 facing downwards).

**Thus, total number of triangles are 20.**

## 2.) How many triangles are in this picture ?

See Answer

### There are a total of 56 triangles in this picture.

**Puzzled How?**

Lets Count.

This is not as simple as the previous one, however we can solve it mathematically by using symmetry.

We can derive a formula as below

Total number of triangles(T) = 2*(A, Number of triangles in one big red triangle) + Number of triangles formed using both red parts(B);

Total number of triangles(T) = 2*(A, Number of triangles in one big red triangle) + Number of triangles formed using both red parts(B);

Number of triangles in one big red triangle can further be calculated as using the below formula.

**Number of triangles in one big red triangle(A) = 2*(C, Number of triangles in one green triangle) + number of triangles formed by combining both green parts(D).**

**Now, lets count the number of triangles in one green triangle**

**C is 9**.

**Now, lets count the number of triangles formed by combining both green triangles.**

**D is 7**.

As we know C and D we can calculate A, ** A= 2*C + D = 2*9 + 7 = 25**

**Now, lets count B(Number of triangles formed by using both red triangles together.**

**so B is 6**.

**Thus, Total number of triangles in the picture T = 2*A + B = 2*25 + 6 = 56.**

## 3.) How many triangles are in this picture ?

See Answer### There are a total of 28 triangles

**How?**

Lets count…

First we will count non-overlapping triangles.

Non-overlapping triangles between 1 & 2: 3

Non-overlapping triangles between 2 & 3: 4

Non-overlapping triangles between 3 & 4: 6

Non-overlapping triangles between 4 & 5: 4

Non-overlapping triangles between 5 & 6: 3

Total number of Non-overlapping triangles: 20

Now, Count overlapping triangles

**Thus, Total number of triangles in puzzle 3: 20+8 = 28**

RORY says

RORY – WHY DO I GET 24 TRIANGLES FOR NUMBER 1?

dillber.com says

you can easily find by visiting http://www.dillber.com/findtriangles

Praveen says

106

Sowmiya says

4th puzzle answer is 60 i guess

niraj says

56 in 4th

eric jeon says

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swapnil says

60 triangles

mateen ahmed ansari says

38 in a figure-2

mateen ahmed ansari says

there is 20 triangles in a figure-1

TM says

I count 26 on the first one.

puzzlersworld says

you are mistaken, you are counting some triangles twice 🙂

Gaurav says

will u please provide the easiest way to solve these type of problem quickly…

Clau Mc C says

1: 20, 2: 30, 3: 28 4:56

puzzlersworld says

@facebook-1071107548:disqus , Answer for the first puzzle is correct, though number of triangles are way more higher for puzzle 2, there are 56 triangles instead of 30, Thanks for your try and we appreciate your comment.

Ceilae Nicole says

the 1st=12 the 3rd=20

the 2nd=12 the 4th=32

puzzlersworld says

@facebook-100003942733752:disqus Thanks for the answers, i updated answer for the first puzzle, there are 20 triangles not 12, check out the solution.