A stick puzzle that seems impossible to solve at first!
Can you convert a triangle made up of 3 matchsticks to four triangles by adding just 3 more sticks?
It is a cute stick puzzle that seems impossible to solve. But don't stop trying, push ahead. Think differently.
The Puzzle
Three matchsticks make a triangle. Add 3 more sticks to make 4 triangles of same size.
Time: 5 minutes.
Comments
It looks like a simple stick puzzle as the given shape is the simplest—only one triangle.
But how can you increase number of triangles to 4? That too when you are allowed only 3 more sticks to add!
Exploration of possibilities—Initial problem analysis
You can add one more triangle by adding two more sticks,
The common stick between two triangles in the figure saves you one stick. Instead of 3 sticks needed to form an isolated triangle, you get an additional triangle by adding only 2 sticks.
But how can you get ON AN AVERAGE one extra triangle with each of 3 sticks you add!
Is it a puzzle impossible to solve? The same doubt momentarily crossed our mind when we first met the puzzle.
What you need for solving this cute stick puzzle is lateral thinking—a way of thinking totally different from the way you are used to think.
Solution to the stick puzzle of making 4 triangles from 1 by adding 3 sticks
At SureSolv, we often approach problem solving and even innovative thinking by deductive reasoning,
A series of pointed questions are asked and right answers are thought out. In the process, focus narrows down towards the solution.
Question 1 generally formed first is,
What are the barriers for solving the problem? What is the main barrier among all?
Answer in this problem is clear.
Allowed number of sticks is less than required for a possible solution.
More precisely,
Limitation on number of sticks is the main bottleneck.
Now at the end of this short barrier analysis, you face an impenetrable wall. No further way forward can be seen.
But you push forward with your questioning.
Question 2,
What is it that is actually responsible for this stalemate? Sure enough I can't change the limitation on number of sticks. But, can I change anything else about the problem?
Parameters or attributes that you can change—a truth
Identification of ALL the parameters or attributes of a problem that you can change almost always leads you to the key attribute and then on to the solution.
Solution to the 6 stick 4 triangles puzzle
The last question precisely is,
Question 3,
What is it that I assume as given and unchangeable about the puzzle (may be without being aware of it) but can still CHANGE to solve the puzzle?
At this point, the solution should be clear to you,
Why! All along we have assumed,
We are to form the new shape on a plane surface like a table top or a flat paper.
Who told us not use a bit of glue to hold the 3-stick joints on top of the existing 3 stick triangular base to form a three-dimensional shape made up of 6 sticks with four triangular faces!
In geometry, this is called a tetrahedron, not a common shape. The triangular base is the given triangle of 3 sticks.
But then, why would you bother with the technical name! All you know is,
I have deviated away from usual thinking to lateral thinking just by deductive reasoning and step by step questioning.
You have taken a systematic analytical approach to problem solving.
End note
For any real life problem situation when you are stuck at an impenetrable wall of a barrier, think deeply on the crucial question,
What is it that I assume as given and unchangeable about the problem (may be without being aware of it) but can still CHANGE to solve the problem?
In all probability you would be surprised to find a new way out to the comforting warmth of the solution.
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