You are here

Add 9 Matches to Make 8 Nodes Matchstick Puzzle

Add 9 Matches to Make 8 Nodes Matchstick Puzzle

Add 9 matches to make 8 nodes in the puzzle figure of a triangle of 3 nodes made up of 3 matchsticks. Time to solve: 5 minutes. Try applying reason.

Matchstick puzzle Add 9 matches to make 8 nodes

In the figure below a triangle is made up of 3 matchsticks. Add 9 more matchsticks to these 3 to make the number of nodes exactly 8. A node is the point of joining of two sticks. There must not be any open node. In other words, at least two matchsticks must join at each node.

Furthermore, one must be able to reach any node starting from any other node.

Add 9 to make 8 nodes matchstick puzzle 1 triangle

Time to solve: 10 minutes.

Solution to the Add 9 matches to make 8 nodes matchstick puzzle

As a painless simple trial, two matches are added to the existing three nodes as shown below.

Add 9 to make 8 nodes matchstick puzzle 2 triangles 4 nodes

What is really achieved by the experiment?


Conclusion 1: by adding two matches to an existing side, a new triangle with one extra node is created.

Effectively then, by adding two matches and creating a new triangle, ONE ADDITIONAL NODE IS CREATED.

It follows by simple arithmetic,

Conclusion 2: By adding 2 x 4 = 8 additional matches each pair of matches forming a new triangle, 4 nodes in addition to the existing 3 are created. Total number of nodes this way becomes 7.

One node then remains to be created by adding only one more matchstick. AND THIS IS IMPOSSIBLE.


Conclusion 3: It is impossible to create 8 nodes by adding 9 matches and creating ONLY NEW TRIANGLES.

This is the discovery of the key constraint.

To overcome the key constraint then,

Conclusion 4: By adding 9 more matches 1 quadrilateral (that must be a rhombus because of equal length oblique sides) must be created along with 3 triangles with 6 matches.

The single additional match unused in the previous experiment of creating 4 more nodes with 8 more matches has now been effectively used for TRANSFORMING AN EXISTING TRIANGLE TO A RHOMBUS THUS ADDING ONE MORE NODE TO THE TOTAL OF 7.

Following is the solution.

Add 9 matches to make 8 nodes solution

Additional 9 matches are colored, 5 as sides of equilateral triangles as green and the rest 4 colored brick red forming a rhombus.

This rhombus with 3 additional matches provided two additional nodes and played the role of the breakthrough component.

End note

No random thinking. Just discovering the clue by a simple trial and then by step by step reasoning.

Do you want to know how to solve difficult problems easily without wasting time on random attempts?

Our new ebook on puzzle solutions by innovative methods will show you just that.

Puzzles for Adults eBook

Puzzles for Adults: 50 Brain Teasers with Step-by-Step Solutions: Boost Your Power of Problem Solving

(Universal link for Apple books, Barnes & Noble, Rokuten Kobo, Vivlio, Angus & Robertson, Tolino, PayHip and others)

You will enjoy solving its 50 challenging brain teasers and at the same time boost your power of problem solving from the innovative step by step solutions rich with new ideas.

The general problem solving techniques are collected first time in a separate chapter.

It's not just solving puzzles. It is also learning innovative problem solving techniques that will change the way you try to solve ANY problem.

You may buy the eBook at Amazon or at Google Play.

Puzzles you may enjoy

Easy to hard brain teasers with systematic solutions

Challenging brain teasers with solutions: Long list.

This will always be the most up-to-date full list with the brain teasers classified into categories that can be browsed separately.

You may also click on the category term link below to enjoy the brain teasers that are classified in the present category.

For example, if the category term link shown below is "Riddle", click on it to go through all the Riddles.