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How many triangles #7

January 20, 2013 by puzzler 1 Comment

1.) How many triangles are there in this hexagon?

how many triangles in this hexagon

how many triangles in this hexagon

Answer with solution

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

Thus, total number of triangles possible in above puzzle are: 18+6+12+1= 37

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How many triangles #6

January 19, 2013 by puzzler 4 Comments

1.) How many triangles are there in this pentagon?

how many triangles in this pentagon

how many triangles in this pentagon

See AnswerHide Answer

There are a total of 35 triangles

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 pentagon answer

Thus, there are a total of 25+ 10= 35 triangles

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How many triangles #5

January 17, 2013 by puzzler Leave a Comment

1.) How many triangles are there in this triangle ?

how many triangles in this triangle

how many triangles in this triangle

See AnswerHide Answer

Answer: There are a total of 47 triangles

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

Thus, total number of triangles in this puzzle are : 21+24+2= 47

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How many squares #4

January 15, 2013 by puzzler Leave a Comment

1.) How many squares do you see in this picture ?

how many squares do you see here

how many squares do you see here

See AnswerHide Answer

Answer with solution

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

Thus, Total number of squares in above puzzle are 19.

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How many triangles #4

January 14, 2013 by puzzler 1 Comment

1.) How many triangles do you see in this image ?

how many triangles do you see  in this image

how many triangles do you see in this image

See AnswerHide Answer

Answer with Solution

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

Thus total number of triangles = 80 + 16 + 16 + 8 = 120.

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How many triangles #3

January 13, 2013 by puzzler 6 Comments

1.) How many triangles do you see in this picture ?

how many triangles do you see

How many triangles do you see

See AnswerHide Answer

There are a total of 84 triangles

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

Thus total number of triangles = 12*4 + 24 + 4 + 8 = 84.

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How many triangles #2

January 12, 2013 by puzzler 1 Comment

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

How many Triangles are there in this picture

How many Triangles are there in this picture

See AnswerHide Answer

There are a total of 92 triangles

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

Thus total number of triangles = 19*4 + 12 + 4 +0 = 92.

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How many squares? Part 3

January 10, 2013 by puzzler Leave a Comment

1.) How many squares are in this picture ?

How many squares do you see in this figure

How many squares do you see in this figure

See AnswerHide Answer

There are a total of 16 squares in above figure.

How?
Lets Count..
5 black colored squares.
1 red colored square.
1 blue color square.
4 small green colored squares in middle.
5 large green colored squares.
Thus, a total of 5+1+1+4+5=16 squares.

2.) How many squares are in this picture ?

[Read more…]

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How many circles?

January 4, 2013 by puzzler 1 Comment

Count the number of circles in the image below.

how many circles do you see in this picture

how many circles do you see in this picture

See AnswerHide Answer

There are a total of 17 circles.

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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Four How many triangles puzzle?

December 29, 2012 by puzzler 16 Comments

1.) How many triangles are in this picture ?

how many triangles are there in this picture

how many triangles are there in this picture

See AnswerHide 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 ?

[Read more…]

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