How to Solve Triangle Puzzle

Have you ever tried solving a puzzle, only to learn that it grows more difficult with each turn? The challenges that each puzzle offers you can change according to the level.  Moreover, these puzzles come in different shapes and sizes, offering different techniques.

A triangle puzzle challenges you to guess the right number of triangles in it. You need to count the triangles to solve the confusion. Although counting looks easy and simple, giving an accurate count is not as easy as it looks. To find the right answer, you can use the formula, p n (n-1)/2. Here, p is the number of horizontal lines, and n is the number of vertical lines. You can put the numbers in the equation and calculate your answer.

The best part of these puzzles is that they boost your mental abilities and power.  And if you think you’re smarter than your friends, this puzzle is the best way to test it. If you want to learn how to solve a triangle puzzle, read this article further.

Table of contents


What is a Triangle Puzzle

A triangle puzzle has several triangles in it. You need to guess the number of triangles present in a single picture.  Of course, the size of the triangle puzzle can vary, but this also changes the number of triangles in it. 

Most importantly, your puzzle will not only feature triangles but other shapes like squares and rectangles. You need to avoid the other shapes and only guess the number of triangles in your puzzle. Make sure to take a good look at the puzzle and consider both the outer layer and inside parts to get an answer that’s close to correct.

How to Solve  a Triangle Puzzle

If you get a triangle puzzle that has three rows and three columns, you can solve it with the simple equation: p n (n-1)/2.  Wondering where this equation comes from?

Well, the value n is that of the vertical lines in a triangle, starting from the bottom to the top edge of the triangle. On the other hand, P is the horizontal line of the triangle that starts from one side of the triangle to the other. In this case, your n is equal to 4, and p is equal to 3. 

You also need to know that a simple triangle has at least one horizontal line and two vertical lines. Similarly, your triangle puzzle of small size or minimum lines should offer you at least three vertical lines and one horizontal line or two horizontal lines and two vertical lines. 

So, put 3 in the place of p in your equation and 4 in the place of 3. After doing this step, your equation will look like this:

3X4 (4-1)/2 

After solving this equation, you get the answer 18. 

This is an easy way to solve a triangle puzzle, no matter how complex, small, or big it is. You can simply keep these rules in mind to get the right answer in the end. 

Sole Your Puzzle without Equation

Solving a triangle puzzle without the equation can be tricky and impossible for most people. This is because, generally, people tend to get confused, and they either forget to count a triangle or count other shapes as a triangle. 

Let's understand how you can see each triangle by yourself.

Begin with 1st Row

You need to start by counting your triangles from the first row. Forget the other parts of your triangle, and only look at the upper row of your puzzle. In this case, the entire first row will make one triangle. Since the 1st row has three columns, each column will make one triangle. This means, if you have three columns, you will have three triangles. In the end, the total triangles you will have are four. 

Merge 1st and 2nd Row

Now, consider the 1st and 2nd row as one. This way, you will have one row and two columns. By combining all the columns, you will have one total triangle. 

Moreover, you need to count each column as one triangle. Since you will have three columns, you will get three triangles. In the end, you will have four triangles.

Consider all Rows as One

Once you consider all rows as one, you will have only three columns. According to this shape, you have to count the entire shape as one triangle. 

Now, you need to count each column as one, giving you three triangles. In other words, by combining all the rows, you get four triangles. 

Combine Columns of 1st  Row

Now, consider the first row and divide it into two parts by combining the columns. You need to consider the two upper columns, the right and center one, as one shape. When you do this and avoid all the other parts of the puzzle, you will see a triangle. 

After this, consider the center and left column as one, which will give you another triangle. In this step, you will have a total of two columns. 

Consider Columns of 2nd Row

Take the first and second row as one, and divide the columns into two parts. This way, you will get a group of right and center columns and another group of left and center columns.  In other words, you will have two triangles in this step based on your chosen shape. 

Look to the Whole Triangle Puzzle

You need to count the triangles by considering all the rows as one, which gives you three big columns. 

Count it by dividing them into a group of left and center columns and right and center columns. Again, you will have two triangles with the help of this shape. 


If you total the number of triangles you have counted through the above-mentioned steps, you get 18. So once you follow these steps, you’re bound to get the right answer. However, this method is extremely tricky from the equation. Not to mention, if you get a triangle puzzle with more than three rows and columns, you’ll have to perform more steps. 

Regardless, you have both options to solve a triangle puzzle, and can use whichever is entirely accessible. 

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