Fun With Matches (Safe!)

[bob012345]

TL;DR: A little geometric puzzle with matches.

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.

 

[DaveC426913]

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

QED

 

[jedishrfu]

Looks like you didn't use the fourth match

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.

 

[DaveC426913]

Looks like you didn't use the fourth match

What do you mean? Bottom left - I flipped it!

 

[bob012345]

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

QED

Funny, but of course the final form of three equilateral triangles must use all the matches.

 

[DaveC426913]

Here is a schematic of the puzzle.

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!

 

[DaveC426913]

Funny, but of course the final form of three equilateral triangles must use all the matches.

So, we're moving the goalposts....

 

[bob012345]

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!

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.)”

 

[bob012345]

Spoiler

 

[DaveC426913]

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.)”

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.)

 

[FactChecker]

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

QED

This reminds me of the saying that the fastest way to get an answer to a question on the internet is to post an intentionally incorrect answer. -- Murphy's Law.

 

[DaveC426913]

the fastest way to get an answer to a question on the internet is to post an intentionally incorrect answer.

Cunningham's Law.

 

[bob012345]

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.)

As I read it, the condition is to form exactly three equilateral triangles without removing any matches. Moving three so they don’t touch the others is removing them from the figure. Likewise, flipping a match is not changing its position because the problem has nothing to do with the design of matches. It could be pencils or sticks or rods.