This puzzle is adapted from 100 Geometric Games by Pierre Berloquin. Twelve matches are arranged as in the image. Can you change the position of four matches to exactly form three equilateral triangles? Do not remove any of the matches.

QED

If you chose the top and bottom matches you have two diamond shapes each with two equilateral triangles.

Then choose outside two matches from one triangle you'd have 3 triangles and 4 matches.

View attachment 369215
I changed the position of four matches to exactly form three equilateral triangles. I have not removed any matches.

QED

So, my solution is

• translate BC northeast by a small amount
• transate DE southeast by a small amount
• translate AF northwest by a small amount
• rotate EF 180 degrees.

Here is a schematic of the puzzle.
View attachment 369217

So, my solution is

• translate BC northeast by a small amount
• transate DE southeast by a small amount
• translate AF northwest by a small amount
• rotate EF 180 degrees.

Be careful how you word your puzzles!

“Can you change the position of four matches so that exactly three equilateral triangles are formed? (Don't remove any matches.)”

The exact wording of the source is as follows;

“Can you change the position of four matches so that exactly three equilateral triangles are formed? (Don't remove any matches.)”

(Facebook is chock full of puzzles like this, and they are all always fraught with ambiguous wording, hidden assumptions and subjective interpretations.)

View attachment 369215
I changed the position of four matches to exactly form three equilateral triangles. I have not removed any matches.

QED

Yes. Are there any conditions I did not meet?

(Facebook is chock full of puzzles like this, and they are all always fraught with ambiguous wording, hidden assumptions and subjective interpretations.)

I'm not bein' a troll. The real lesson in these puzzles has nothing to do with the answer itself - it has everything to do with the assumptions in the answers - but just as importantly, the assumptions in the questions themselves.

That's my point. Ambiguity leads to subjective intepretation.

Yup. That's an interpretation.

Yup. So is that.

Yes. Which would still make my answer valid. Pencils and sticks can still be rotated 180 degrees.

I'm not bein' a troll. The real lesson in these puzzles has nothing to do with the answer itself - it has everything to do with the assumptions in the answers - but just as importantly, the assumptions in the questions themselves.

Ect…it would be no fun at all. BTW, the initial image is a big clue to how to approach the problem. It’s one whole figure.

What is "exactly three equilateral triangles"? Even that requires lot of assumptions. You made them differently, or you wouldnt have had to state them expicitly.

What is "do not remove"? My answer did not remove them - it moved them - a legal operation.

In fifty years, many people have gotten a lot more sophisticafed at problem-solving. What wrked then may not work anymore.

That's a total of seven words. Eminently reasonable.

My solution doen't require me to add more canvas, as yours does.

But the problem itself implies that 3 matchstick touching end-to-end counts as a valid equailateral triangle. So that is a level of pedantry I would consider a bridge too far.

I do not consider my solution to violate any implied rules. It's a valid solution that highlights ambiguity in problem statements. Having done a lot of these, I can tell you, the trick is often in those very assumptions.

That being said, I might argue that bob012345's solution is the more elegant solution.

Our version was slightly different from the one in the linked article. We bent our paper clip launcher so that one prong stuck upwards at an angle, and slid that prong between the aluminum foil and the match stick. This both aimed the rocket and provided the exhaust vent for the propulsion gases. That is, we didn't use a safety pin to make the exhaust vent separately.

As I mentioned, these puzzle now show up online so often that a new context is formed organically. A lot of puzzles rely on the leaky margins of specifications to solve.

For example - the classic matchstick puzzle: can you make four identical equilateral triangles using only six matchsticks?

I agree with this. The era and context provided additional ... context, of which we are bereft.

As I mentioned, these puzzle now show up online so often that a new context is formed organically. A lot of puzzles rely on the leaky margins of specifications to solve.

For example - the classic matchstick puzzle: can you make four identical equilateral triangles using only six matchsticks?