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# 4 Identical Triangles

### #31

Posted 27 November 2007 - 08:38 PM

move the match to make somthing like this 4 /_ (it`s mean four triang.)

### #32

Posted 01 December 2007 - 10:06 PM

**.**

*S*### #33

Posted 21 February 2008 - 01:07 AM

### #34

Posted 11 March 2008 - 05:30 AM

These kind of riddles suck.

### #35

Posted 11 March 2008 - 05:36 AM

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

/_/_ /_/_

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.

### #36

Posted 18 March 2008 - 02:18 PM

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.

### #37

Posted 25 April 2008 - 02:42 AM

silly but new thought line.

### #38

Posted 25 April 2008 - 03:12 AM

### #39

Posted 01 May 2008 - 12:13 PM

4 Identical Triangles- Back to the Matchstick Puzzles

Move one matchstick to get 4 triangles.Spoiler for Solution

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.

### #40

Posted 27 May 2008 - 12:09 AM

**S**which is impossible. You show them the solution and tell them you asked for four triangle...

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