How to solve triangular matchstick number in Python

In this tutorial, let’s see how to solve the triangular matchstick number in Python. It is a well-known problem and is as follows:
Given the number of sub-triangles in the base layer of the bigger triangle, find the total number of matchsticks required to build the overall triangle until there is a single triangle at the top. You can refer to the below picture for more clarification.

solve triangular matchstick number in Python

In the above picture, consider each triangle to be made of 3 matchsticks. So the objective of the problem is to find the total number of matchsticks required to build the whole triangle. Before we look at the solution, take a few moments to think of a possible solution.

The idea behind the solution:

It is quite clear from the picture that the numbers of triangles at each level decreases by 1 starting at the bottom. If the bottom layer has T sub triangles, the layer above it will have T – 1 sub triangles and so on until the topmost layer has 1 triangle. So it is clear that the final triangle will have T + (T – 1) + (T – 2) + … + 1 sub triangles which is also equal to (T * (T + 1)) / 2. Multiply it with the number of sticks required for each sub triangle and you will have the final answer. So the final solution comes down to one simple formula: 3 * (T * (T + 1)) / 2.

How to solve triangular matchstick number in Python:

# Number of sub triangles in the base layer
T = int(input())

# Total number of sub triangles
subtriangles = (T * (T + 1)) // 2

# Total number of sticks required
stick_count = subtriangles * 3

print("The number of matchsticks required is", stick_count)

As you can see, we have solved the problem quite easily. I hope you found this article helpful in solving the problem.

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