(14 votes, average: 3.50 out of 5)1.) How many triangles are in this picture ?
how many triangles are there in this picture
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 ?
how many triangles are there – puzzle 2
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.
how many triangles are there 2 – answer
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);
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
number of triangles in green triangle
Now, lets count the number of triangles formed by combining both green triangles.
number of triangles formed using both green parts
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.
number of triangles formed using both red parts
Thus, Total number of triangles in the picture T = 2*A + B = 2*25 + 6 = 56.
3.) How many triangles are in this picture ?
how many triangles are there – puzzle 3
There are a total of 28 triangles
How?
Lets count…
First we will count non-overlapping triangles.
how many triangles are there – puzzle 3 – answer
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
counting the number of overlapping triangles
Thus, Total number of triangles in puzzle 3: 20+8 = 28
4.) How many triangles are in this picture ?
how many triangles do you see in this figure
RORY – WHY DO I GET 24 TRIANGLES FOR NUMBER 1?
you can easily find by visiting http://www.dillber.com/findtriangles
106
4th puzzle answer is 60 i guess
56 in 4th
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60 triangles
38 in a figure-2
there is 20 triangles in a figure-1
I count 26 on the first one.
you are mistaken, you are counting some triangles twice 🙂
will u please provide the easiest way to solve these type of problem quickly…
1: 20, 2: 30, 3: 28 4:56
@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.
the 1st=12 the 3rd=20
the 2nd=12 the 4th=32
@facebook-100003942733752:disqus Thanks for the answers, i updated answer for the first puzzle, there are 20 triangles not 12, check out the solution.