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4 Identical Triangles


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I understand the "trick" behind the puzzle. However, the title needs to be changed to "4 triangles" instead of "4 identical triangles. Because it doesn't matter how you explain the joke...in order for something to be identical to something there has to be more than one of it. there is no way to get 4 identical triangles from moving one matchstick in this puzzle.

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I understand the "trick" behind the puzzle. However, the title needs to

be changed to "4 triangles" instead of "4 identical triangles. Because

it doesn't matter how you explain the joke...in order for something to

be identical to something there has to be more than one of it. there is

no way to get 4 identical triangles from moving one matchstick in

this puzzle.

1: I've already demonstrated a non-joke solution that satisfies the 4 identical triangle requirement.

2: Your reasoning is also flawed, because x = x. In other words, any given thing is identical to itself.

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The solution is to make a 3 dimensional pyramid. There will be 4 identical triangles with the same amount of sticks.

Well, the problem statement didn't limit itself to 2 dimensions, but I don't see a way to do such a thing with only a single matchstick move.

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nonsense. 2 lines form an angle... not a triangle this is a ridiculously false reference.

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.

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I'd first like to point out that the statement:

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.

is not strictly true. If I'm looking at this correctly, it is only true in the case where the known angle is the included angle of the two known sides, if the angle is included by the shorter of the two known sides and the unknown side, or if it is a right triangle.

In this case, though, the angle is included, so the statement is true. Of course, one would assume from the problem that each side of the triangle is supposed to be represented by a specific matchstick. One could also assume, though, that the problem intended for four triangles to be formed geometrically, not represented by the numeral 4. Since it's impossible for a solution to satisfy both these assumed properties, it makes just as much sense to count four triangles as being those uniquely determined by the matchsticks, even if there are not match sticks representing each of the individual sides, as it does to count the posted solution.

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4 Identical Triangles - Back to the Matchstick Puzzles

Move one matchstick to get 4 triangles.

post-2-1175381105_thumbgif

4 Identical Triangles - solution

post-2-1175381180_thumbgif

There is a solution in which you would get 4 identical triangles by moving one match. Take one match from the left, break it into three equal piecees and arrange them into an inverted trianle, inside the triangle on the right. (See sketch.) My appologies for the crudity of the sketch, I didn't have time to build it to scale or to colour it. ;)

post-6456-1209639990_thumbjpg
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You goofed the setup. You're supposed to ask for them to move one match to get four triangle. They assume you mean four triangleS which is impossible. You show them the solution and tell them you asked for four triangle...

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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.

that doesnt work at all because it says to move one match stick

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It's an old trick. :P

but identical... its not really identical if you have only one triangle and all "4 triangles" refer to the same one

Edited by FreudianComplex
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