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### Answer with Explanation

Answer is 54325

How?

Just keep appending the new number to the previous answer 🙂

by Ankur 4 Comments

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Answer is 54325

How?

Just keep appending the new number to the previous answer 🙂

**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**

by Ankur 2 Comments

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Given

6 – 1 x 0 + 2 / 2

= 6 – 0 + 1

= 7

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Given

11×11 = (1+1)*(1+1) = 4

12×12 = (1+2)*(1+2) = 9

13×13 = (1+3)*(1+3) = 16

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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

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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

Looking at the symmetry, we can divide this triangle in 5 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.

**Number of triangles in one square**: 8(non overlapping triangles) + 8(overlapping triangles with middle lines a part of the triangle) =**16*5 = 80**

**Number of triangles by taking two squares(one middle and one other) at a time:** 4*4(there are four such combinations) = **16**

**Number of triangles by taking (only) three squares(one middle and two others) at a time:** 4(all squares should be a part of the triangle) *4(four such combinations) = **16**

**Number of triangles by taking 4 squares together: ** 2 *4(four such combinations) = **8**

**How?**

Lets count…

Looking at the symmetry, we can divide this triangle in 4 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.

**Number of triangles in one square**: 8(non overlapping triangles) + 4(overlapping triangles with middle lines a part of the triangle) =**12**

**Number of triangles by taking two squares at a time:** 6(try a little harder, you will fidn these) * 4(there are four such combinations) = **24**

**Number of triangles by taking (only) three squares at a time:** 1(all squares should be a part of the triangle) *4(four such combinations) = **4**

**Number of triangles by taking all squares together = 8**

**How?**

Lets count…

Looking at the symmetry, we can divide this triangle in 4 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.

**Number of triangles in one square**: 8(non overlapping triangles) + 8(overlapping triangles with diagonal a part of one of the side) + 3(diagonal is perpendicular to one of the side of the triangle) =**19(You can get it correct after a little hard try)**

**Number of triangles by taking two squares at a time: **3(common side of square is perpendicular) * 4(there are four such combinations) = **12**

**Number of triangles by taking three squares at a time:** 1(all squares should be a part of the triangle) *4(four such combinations) = **4**

**Number of triangles by taking all squares together = 0**

**How?**

1 black circle in the middle(easily visible to all)

Now move a little away from the screen(16 more circles will be visible easily).

Thus, there are a total of 17 circles.

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