How Many Triangles are There

For lovers of brain teasers, here’s another one to exercise your brain with. Did you enjoy the last set of brain teasers we posted?  This particular puzzle was posted by a certain “Doctor Asky” on Facebook, and of course, there were a myriad, of answers. However, we’ll not be exploring those many answers, only the right one.

Take a few minutes and think about it. After you’re sure you have the right answer? Then we’discuss the solution to the triangle problems.

There are more than one ways to go about getting the answer. There’s the graphical method. That is where you’ll actually count the number of triangles. There are also mathematical manipulations with which to get the answer.

There are actually a lot, some are quite complex that it would require some patience to understand, except you’re familiar with such mathematical problems. So we’ll just go with the simple mathematical method to find the solution.

Okay, there are 24 triangles in the picture.

Step 1: Count the number of column and rows. Columns are the vertical spaces while rows are the horizontal spaces.

From this triangle, we have 3 columns and four rows.

Step 2: Now we’ll get a sum of the column number.  Remember we have three columns. That would give us 1+2+3=6.

Step 3: We’ll multiply the sum of the column number by how many rows we have in the triangle.

6 X 4 = 24. We have 24 triangles in this picture.  You don’t believe right, then let’s take a look at it graphically or count it manually.

This method can be used to solve problems of triangles like this. Will it work for a quadrilateral? (a four shaped figure). There’s only one way to find out.


There you have it. The mathematical method is better because you can apply to a triangle of infinite numbers. Without having to undergo so much stress.

I feel like your brain has had to do some work. Here’s one more brain teaser.

Just for some extra fun. Solve this puzzle,

Spot the difference between this two very similar pictures



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