4 Identical Triangles

[rookie1ja]

4 Identical Triangles - Back to the Matchstick Puzzles

Move one matchstick to get 4 triangles.

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

Pls visit New Puzzles section to see always fresh brain teasers.

4 Identical Triangles - solution

[Guest]

Umm... question if you do 4 identical triangles shouldn't you have 4 acutal triangles not a 4 then a picture a of triangle. Could you explain how this is (what you showed me) the correct answer and how it is logic promblem and not just a math joke.

[Guest]

Umm... question if you do 4 identical triangles shouldn't you have 4 acutal triangles not a 4 then a picture a of triangle. Could you explain how this is (what you showed me) the correct answer and how it is logic promblem and not just a math joke.

it's impossible to get 4 actual triangles with the current setup, so the only way to get 4 is to actually make a 4.

[Guest]

How about a diamond with a cross in the center?

[Guest]

yes that would be 4 triangle but the current arrangement of the triangle doesn't allow the formation of the diamond.

[Guest]

Site Admin,

I don't really understand your solution, could you please explain it?

[rookie1ja]

it's just a little joke ... child's play ... you create number "4" from the first triangle and keep the second triangle thus it could be 4 triangle

[Guest]

try a 3D figure n u'll find the solution

[Guest]

Umm, not a logic puzzle, however it is possible to move one matchstick and get 4 triangles; just not 4 identical

[Guest]

Solution process: Hmm... This is pointless, but... Lost my idea. I'm going insane! Maybe... I'll look at the solution! Hahaha... what a nice joke.

[Guest]

okay! okay!

[Guest]

I get it...thats funny!!!!! lol

[Guest]

It won't allow me to upload a file. I drew out the solution to the problem using paint. Says it won't allow a bmp extension. Any help appreciated.

[rookie1ja]

It won't allow me to upload a file. I drew out the solution to the problem using paint. Says it won't allow a bmp extension. Any help appreciated.

convert it to jpg or gif ... try to minimize the size as well

[Guest]

Some of the problems like this are cute, but this is just plain dumb. Reminds me of a not funny version of the 'riddle':

Peter: "You have two babies, and one has to die. Which one do you kill."

Brian: "That's not a riddle, that's just horrible."

Peter: "WRONG! The ugly one."

[Guest]

ermm ok thats strange I was thinking more on the lines of 4 triangles not the number 4 then a triangel lol gud 1 tho

[Guest]

I don't think the joke really works. If the puzzle was to move one matchstick to get 4 triangle, then sure. But the solution doesn't give 4 identical triangles.

[Guest]

haha- lateral versus literal, like it!

[Guest]

It is easy, make a 3d pyramid.

[Guest]

a 3rd pyramid isnt a solution. it says "move ONE match to create FOUR IDENTICAL TRIANGLES". no solution for that here as of yet. its silly, but i felt i had to pointit out since there are so many solutions here that arent for this teaser. nobody is following the discription

[Guest]

you can do the diamond form, moving 2 stick

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that's why i think, it doesn't have a solution, or is the wrong question

excuse my english, i need to practice

[Guest]

Despite there existing a joke solution, there also exists a real solution.

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That crude ASCII drawing of it might not make it clear, but if you draw it out yourself you'll see. If you just take one of the outside sticks and put it below, at the same angle, such that its top end is touching the point where the original triangles meet, then you have your solution: 4 identical triangles in 1 move.

I think people were just getting stuck because they assumed that a triangle must have three lines. But if you took basic Geometry, you should know that if you know the size of one angle and the length of two sides, then you can figure out the other two angles and the other side. Now, assuming that the matchsticks are all of equal length (which they are in the original image for the puzzle), then we know that in fact all the angles are 60 degrees, because this is true of any triangle whose sides are all of equal length (the angles of any triangle must add up to 180 degrees, and if all the sides are equal then all the angles must be equal, so 60 * 3 = 180 is the only possibility). Therefore, if we preserve the same orientation of the matchstick when we move it, then the new angle will also be 60 degrees. From here, it's a rather simple matter to mathematically prove that all four triangles are in fact identical.

[Guest]

Ok, I've got the solution.

matchstick.JPG[/attachment:12be6]

[Guest]

Penguin wrote:

Despite there existing a joke solution, there also exists a real solution.

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I think people were just getting stuck because they assumed that a triangle must have three lines. But if you took basic Geometry, you should know that if you know the size of one angle and the length of two sides, then you can figure out the other two angles and the other side.

I had considered this solution as well, however, I have to disagree with Penguin's line of logic. A quick query at dictionary.com reveals that a triangle is "a closed plane figure having three sides and three angles."

Each of Penguin's proposed triangles have only two sides and one angle, which is actually defined as an angle, not a triangle.

If you took basic geometry, you would probably also remember that when proving triangle properties, you actually need a triangle to prove. I don't recall any proofs that took an angle, added an arbitrary third side, called it a triangle and proved its properties. Granted we know the length of two sides, and the angle can be inferred from fact that the original configuration of the matchsticks suggest the triangles are equilateral, we have no proof what the length of the third side would be. Although we can assume (if you took geometry, you might have learned not to make assumptions) that the third side would be composed of matchsticks of the same size, we cannot prove this. This would require the addition of three matchsticks into the problem, which the original statement didn't mention. Again, we could assume that because the original problem didn't state "and you can't add any extra matchsticks," I think I mean to drive home the point how improper, logically, assumptions are.

Thus, Penguin's solution only results in one triangle.

[Guest]

Penguin wrote:

Despite there existing a joke solution, there also exists a real solution.

/_/_


/_/_

I think people were just getting stuck because they assumed that a triangle must have three lines. But if you took basic Geometry, you should know that if you know the size of one angle and the length of two sides, then you can figure out the other two angles and the other side.

I had considered this solution as well, however, I have to disagree with Penguin's line of logic. A quick query at dictionary.com reveals that a triangle is "a closed plane figure having three sides and three angles."

Each of Penguin's proposed triangles have only two sides and one angle, which is actually defined as an angle, not a triangle.

If you took basic geometry, you would probably also remember that when proving triangle properties, you actually need a triangle to prove. I don't recall any proofs that took an angle, added an arbitrary third side, called it a triangle and proved its properties. Granted we know the length of two sides, and the angle can be inferred from fact that the original configuration of the matchsticks suggest the triangles are equilateral, we have no proof what the length of the third side would be. Although we can assume (if you took geometry, you might have learned not to make assumptions) that the third side would be composed of matchsticks of the same size, we cannot prove this. This would require the addition of three matchsticks into the problem, which the original statement didn't mention. Again, we could assume that because the original problem didn't state "and you can't add any extra matchsticks," I think I mean to drive home the point how improper, logically, assumptions are.

Thus, Penguin's solution only results in one triangle.

Well, you made two mistakes here.

The first is that you claim you cannot prove the length of the third side, but in fact you can, as I have already explained, but I will reiterate for you. We know the angle is 60 degrees, and we know each side is the same length. We do not know the actual length of each matchstick, but we know that they are all of equal length (which you can tell from the original problem's image). However, it is entirely irrelevant what their actual length is. Suppose that they were 10 (of your favorite units). Thus, since both sides are 10, and your angle is 60, then the ONLY possible length for the remaining side is 10. Try the math out yourself if you don't believe me. Then change the matchstick size to 100 or any other number you want, and it still comes out the same. We know the sides are equal, and the angle is 60, thus we know it is an equilateral triangle and the remaining side can only be the same length as the other two sides.

Also, I'd like to mention that your calling it an "angle" is incorrect, because an angle has two sides of arbitrary length, while we know for a fact that these sides are of finite length, and in fact the same length.

Your second mistake is your taking this concept of a "triangle" far too literally. Here is a helpful fact for you: There is no such thing as a "triangle". A "triangle" is simply a name given to a particular "shape". A "shape" does not exist in reality, but exists only in our minds. It is merely a pattern of light that we have evolved to recognize because it helped us survive. Take any three "points" (i.e. a visible mark whose location can be specified by a single pair of coordinates, or a three-tuple if you're dealing in 3 dimensions) and you have yourself a triangle. However, if you don't want to see it as a triangle, then you don't have a triangle. Like I said, it's all in your head. The concepts of shapes, colors, and distinct physical objects are all just abstract simplifications in our minds. If we went around seeing what's really there, we'd go insane. If you are interested in what you're "really" looking at, then I suggest you study quantum physics.

Anyway, my point is, just because a third line is not drawn in front of you doesn't mean that you are not looking at a triangle. A triangle is just a pattern, and a pattern exists as long as you have enough information to prove that it exists, which we do. In fact, all you need to prove the existance of a triangle is three points. If you have three points, then you have a triangle. And we do have three points: One where the two matchsticks meet, one at the end of one matchstick and another at the end of the other matchstick.

Now, you quoted me this definition: "a closed plane figure having three sides and three angles." If you truly understood math, you would know that this is not a definition of an actual entity existing in the real world, but rather an abstract concept that makes it easier for humans to make calculations. I believe Einstein explained it best: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."