Geometric Game: Fun With Matches (Safe!)

[DaveC426913]

I believe so, yes. How is that leaky though?

The puzzle works better presented visually, like this:

Can you arrange six matchsticks to form exactly four equilateral triangles?

The presentation tends to put imaginary constraints on the solution, even if we don't realize it. In this case, it encourages us to think in only the two-dimensional plane of the page.

Skilled thinkers will see through this trick and find the solution that is not constrained to the page, as you did.



Here is another one:

Join these nine dots with exactly four straight lines, without lifting your pen off the page:

Spoiler: Solution

In this case, the rendering of the puzzle encourages you to literally "think inside the box". The constraint that "you cannot use the space outside the nine dots" is imaginary, self-imposed.

Now, notice that your solution to the original puzzle does a similar thing - it breaks out of the imaginary constraint of the puzzle's own boundaries:

(you literally added more whitespace to the left)
Perfectly valid.

And of course, you also saw through the imaginary constraint that all the triangles will be the same size - something that often trips up newbies.




As for my solution:

I did not remove any matchsticks.

Nowhere does it say that "do not remove any matchsticks" means "they all must be connected in one object". That is an imaginary constraint you put on yourself and your solutions.

Even if I granted that constraint, I could have just as easily produced this:

Granted yours as still the more elegant solution, but all of them are about assumptions and constraints.



This is where these puzzles live. In the leaky margins of our assumptions, preconceptions and self-imposed, imaginary constraints.

 

[bob012345]

@DaveC426913 , while you are mathematically correct and from a purely mathematical point of view, you obeyed the rules, your solution exists along with a literal infinite number of similar solutions which should be a clue that is not the unique solution the author had in mind. These aren’t intended to be rigorous mathematical formulations. How would you have written this puzzle if you were its author? Can you imagine how this puzzle would read if written by someone like Andrew Wiles! :)

 

[DaveC426913]

@DaveC426913 , while you are mathematically correct and from a purely mathematical point of view, you obeyed the rules, your solution exists along with a literal infinite number of similar solutions which should be a clue that is not the unique solution the author had in mind.

There's the crux, isn't it?

So, the puzzle is less "can you find a solution" and more "can you find the solution I intended"

It's like two types of video games - an open world versus a closed world. An open world is where you find your own solution. A closed world you will run into walls until you find the single solution allowed.

_{(at least, I assume it is. I play exactly one video game: Cities: Skylines)}

These aren’t intended to be rigorous mathematical formulations. How would you have written this puzzle if you were its author? Can you imagine how this puzzle would read if written by someone like Andrew Wiles! :)

I said so in post 16. All it needs is the conditions you thought were implicit:

"using all matches; create no extraneous shapes"

That's seven words.

 

[bob012345]

There's the crux, isn't it?

I said so in post 16. All it needs is the conditions you thought were implicit:

"using all matches; create no extraneous shapes"

That's seven words.

I understand but I think part of the game is to figure that out. It took me a few hours to get to the second assumption. It took only a few minutes once I realized it.

 

[DaveC426913]

It took me a few hours to get to the second assumption.

How long did you spend on this puzzle??

 

[BWV]

The puzzle works better presented visually, like this:
View attachment 369248
Can you arrange six matchsticks to form exactly four equilateral triangles?

That is not hard, just make a pyramid

 

[Gavran]

I said so in post 16. All it needs is the conditions you thought were implicit:

"using all matches; create no extraneous shapes"

That's seven words.

Agree with the above.

“Find x where x²=4” versus “Find x where x²=4 and x>0"; two different problems with two different sets of solutions.

Or post #28

can you make four identical equilateral triangles using only six matchsticks?

versus post #31

Can you arrange six matchsticks to form exactly four equilateral triangles?

; also, two different problems with two different sets of solutions.