In the matchstick figure, move 4 matches to make 5 triangles with no match kept hanging not being a part of a triangle. Time to solve 15 minutes.
I have given a little more time to solve this puzzle simply because it stopped me in my thinking tracks for a moment. You may though easily solve it well within 15 minutes.
Solution of move 4 matches to make 5 triangles matchstick puzzle: Falling back on a time-tested method
As I looked at the puzzle figure on my laptop screen trying to find a quick solution, I realized that within a minute solution is eluding me.
Not a surprise.
I am 70, just got out of COVID with a dullness in my body and mind and more importantly, the first necessary job in solving this puzzle is to imagine a figure of 5 triangles with only 9 matchsticks!
My old tired mind refusing to juggle with the possible configurations, my advisor mind reminded me of the old method that never failed in this type of situations.
I reached out for my well-worn equally old matchbox and spread its little mysteries of sticks on my long notebook.
Making and unmaking figures with actual matchsticks never fails to give me a quick insight into the solution.
When I manhandle the matchsticks, the rules and techniques of matchstick puzzle solving automatically get fired up in my mind. Visual intuitive and conscious mind reasoning efforts start working together.
Solving a tricky matchstick puzzle invariably needs image manipulation. Playing with actual physical matchsticks always gives me a quick solution with the bonus of an unexpected additional pleasure.
My recommendation to you: Keep a box of matchsticks handy and play with actual matchstick shapes whenever you feel like it.
Solution of move 4 matches to make 5 triangles puzzle: Number of matchstick analysis for visualizing the solution figure
As a self-proclaimed problem solver, I always go first for knowing and analyzing the final solution destination that I have to reach.
I have named this tendency with a few more embellishments as the END STATE ANSALYSIS APPROACH OF PROBLEM SOLVING. It follows simple common sense: you need to know where you have to go.
So what will be the final solution figure for this puzzle?
A quick calculation tells me, 5 independent triangles need (3 x 5 = 15) matches and you have only 9.
So you have to somehow create a matchstick triangle figure with 9 matches that has 6 matchsticks each common between at least two triangles.
A tall order.
And at start, I was stuck at this point of visualizing the final solution figure!
When I opened my old matchbox and took out the matches, forming the final solution figure was automatic and took just about 30 seconds.
And why not! When you have to imagine a matchstick triangle solution figure made up of 9 matches with 6 common sides, the figure must be the MOST COMPACT matchstick triangle figure made of 9 matches!
Without much else in my mind, I started with a 2-match side triangle first and then connected all the match ends inside the triangle. This must be the MOST COMPACT 9 match figure. Have a look at it below.
How many triangles do we have here? You may count 4, but being more experienced, I recall that there is no restriction on the size of the 5 triangles to make. So I also count the larger outer 2-match triangle as 1 more making total count as 5.
This familiar figure itself is our final solution figure.
In making this figure not for once I have thought about the initial puzzle figure from which I have to make this final figure.
That's the trick. When forming the details of the final solution focus your whole attention only on what actually is needed for solution without thinking at all of HOW YOU WILL GET TO THE SOLUTION.
Solution to move 4 matches to make 5 triangles puzzle: Finding matchsticks common between initial and final figures
For the second part of the puzzle also I adopt a never-failing method that you might call a clever trick!
Instead of trying to urge my tired neurons to work harder, I create the initial and final figure side by side and compare the two figures to identify precisely the matchsticks that are common between the two figures.
Go on, do it for yourself.
Now with my two figures side by side, I reason like a child,
If I have to move 4 matches out of 9, then the rest 5 matches must not be touched at all! All of them must be kept fixed.
Aside: I implore you never to underestimate the intelligence of a child. I have a firm belief that children are generally far more intelligent than the adults.
Well then, I have to keep 5 matches fixed when making the solution from the puzzle. That means simply,
I have to find out VISUALLY 5 matches that are COMMON between the final solution and initial puzzle.
And it again takes just about a minute to identify the 5 matches common between the two figures. By common I mean, these 5 matches form a structure that is exactly same in both figures.
The 5 common matches are colored red. I personally don't like red, but possibly you like it. So it is red.
As we adults say, now it's child's play to move the rest 4 matches and form the final figure from the puzzle. Moves are shown.
I should mention here that comparing the final solution figure with the initial puzzle figure in this second part of the solution is not really a trick. It is the second part of nothing other than END STATE ANALYSIS APPROACH again. It bypasses the need for all detailed thinking.
My bonus: it has been a real pleasure of physically playing with my old friends matchsticks.
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Move 4 matches to make 5 triangles matchstick puzzle