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### Answer with Explanation

Answer is 6.

**How?**

It is the simple subtraction as we used to do in our early maths classes in our childhood, so just reminds us of those days of taking carry and subtracting.

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Answer is 6.

**How?**

It is the simple subtraction as we used to do in our early maths classes in our childhood, so just reminds us of those days of taking carry and subtracting.

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Answer is 9.

**How?**

Here, every element in second row = corresponding column element in first row * 2.

Similarly every element in third row = corresponding column element in first row * 3.

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Answer is 30.

**How?**

Sum of the numbers on vertices of a triangle should be 90, i.e. 20 + 40 + ? = 90 => ? = 30.

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Answer is 6.

**How?**

Here, Number in a block is sum of the number on the top and right block so 7 = 1 + ?, hence ? should be 6.

**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?**

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)

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**

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.

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Answer is 9.

**How?**

Here, every middle element is the sum of the other two so answer should be 6+3 = 9.

**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).

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