Bombadil
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Hi there!

A few days ago a friend of mine told me this problem and I thought I'd share it with you.

We have a star:

and within it five triangles.

Tracing two straight lines you should be able to count ten triangles.
They have to be entire. For example:

is only ONE triangle,

and this are only two.

The problem HAS a solution but I know only one person who has find it in half an hour. There is no trick like using the borders of the paper or anything else, the problem is as it is.

If you find the solution, don't post it (I don't know if images can be inside that secret things).

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[Last edited by Bombadil at 08-31-2005 09:43 AM : Yes, you can put secret images]

Mattcrampy
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What do you mean by 'two straight lines'? I'm assuming that your examples are along the lines of what you mean, that the lines are allowed to bend so long as each segment is straight and they all join up, because if so, I'd just do two stars.

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MeckMeck GRE
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File: star2ju3.jpg (3.3 KB)
Downloaded 193 times.
License: Other
From: Unspecified

I think I´ve got it ! (Attatched is my solution ; SPOILER WARNING)

Bombadil
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Mattcrampy wrote:
What do you mean by 'two straight lines'? I'm assuming that your examples are along the lines of what you mean, that the lines are allowed to bend so long as each segment is straight and they all join up, because if so, I'd just do two stars.

I don't know if I understand what do you mean but:
straight: Extending continuously in the same direction without curving: a straight line.

Simply two lines.

The examples are simply to clarify the situation, in some problems, the first one might count like two and the second one might count like three (because you might wanna count the little ones and the big one).

Btw, how do you make another star with two lines?

Bombadil
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MeckMeck GRE wrote:
I think I´ve got it ! (Attatched is my solution ; SPOILER WARNING)

WRONG:

MeckMeck GRE
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Your right, is really wrong, if you count EVERY triangle you get more than 10 ! (If you hence the hidden triangles)

Bombadil
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MeckMeck GRE wrote:
Your right, is really wrong, if you count EVERY triangle you get more than 10 ! (If you hence the hidden triangles)

That's why I posted the images with the explanation of what does and what doesn't count as a triangle. Notice that if you count all triangles in a single star there are ten triangles. ^^

stigant
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Your examples are still confusing. For example, in the first example, you say that there is only one triangle. I see two. Now, I'm willing to accept, for the purposes of this problem that one of them won't count as "Entire". But which one (the large triangle or the small triangle formed in the corner) doesn't count and why is it not "Entire"?

Part of the problem is that I don't understand what you mean by Entire. This may be a language problem. To me, entire means complete, whole, all there. To me, the triangles in your first example are "entire" because there are three sides and three angles bounding each of the triangles.

Secondly, do you mean by "trace two lines" to "add two lines to the figure so that there are exactly 10 Entire triangles in the diagram"? When I think of trace, I think of going over lines that are already there, but I think this type of problem usually involves adding lines to the picture.

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Bombadil
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I'm sorry, this is all caused by my bad English.

When I say entire I mean that there is nothing that cuts him or so. In the first example the big one doesn't count because there's a line cutting it. In the second example only count the two little ones because the big one is cut too.

Yeah, by tracing I mean adding. Isn't that correct?

Doom
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I've seen the answer somewhere and I remember the general idea, but I still can't figure out how to actually do it. (I don't remember it that well)

By the way, do new triangles outside the star count?

Bombadil
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Doom wrote:
By the way, do new triangles outside the star count?

As long as they have three sides...

stigant
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I'm sorry, this is all caused by my bad English.

Well, somewhat, but I can see what you were trying to say... Entire = Whole, and you mean whole as opposed to "cut in to bits". Your English is fine, you just looked at the situation differently than I did. Frankly, the English language itself is just as much to blame as any of us.

I just gave this problem to one of my Geometry classes, and I called the triangles "Empty" because they don't have any lines going thru them.

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Mattcrampy
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Oh, I see. You have to add two lines to the original star. Right.

Edit: I can get 9, and have lots of alternatives for 8, but ten still alludes me.

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[Last edited by Mattcrampy at 08-31-2005 08:17 PM]

Bombadil
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stigant wrote:
I just gave this problem to one of my Geometry classes, and I called the triangles "Empty" because they don't have any lines going thru them.

Wow! Empty, I love that way of saying it.

Mattcrampy wrote:
Edit: I can get 9, and have lots of alternatives for 8, but ten still alludes me

Eight and nine are kind of easy to find, but I don't know why the solution is very ... (i don't know the word) difficult to catch.

Doom
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I can also get 9 in many different ways, but I'm failing to find the 10-part solution...

I just realized, that I have not seen the answer to this... I mistaked it for another similar kind of puzzle. It's a lot easier.

Basically, you have to cut a crescent moon into 6 parts with 2 straight lines. Sizes and shapes don't matter and areas outside the picture don't count.

Tim
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Doom wrote:
Basically, you have to cut a crescent moon into 6 parts with 2 straight lines. Sizes and shapes don't matter and areas outside the picture don't count.

I still don't understand the original question. But cutting a cresent moon into 6 parts with 2 lines isn't really hard, is it? As long as these parts do not have to be symmetrical or the same size, it's quite simple?

Doom
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Tim wrote:

Doom wrote:
Basically, you have to cut a crescent moon into 6 parts with 2 straight lines. Sizes and shapes don't matter and areas outside the picture don't count.

I still don't understand the original question. But cutting a cresent moon into 6 parts with 2 lines isn't really hard, is it? As long as these parts do not have to be symmetrical or the same size, it's quite simple?

Yes, it's quite easy. You can try it for yourself to see.

What part of the original question you don't understand?

Tim
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Doom wrote:
Yes, it's quite easy. You can try it for yourself to see.

I figured the answer before I wrote my last post.

What part of the original question you don't understand?

Sadly, all of it. My bad English... (No, no need to explain it to me now... I'm currently too tired anyway...)

-- Tim

Bombadil
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By crescent moon you mean a moon that is still not at crescent. I mean not half a circle...

Doom
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File: Moon.JPG (5.2 KB)
Downloaded 102 times.
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I mean a picture like the attached image. I've found 2 different solutions to it.

But that's not so important. Let's stay on topic.

Schik
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I found a solution that gives me 10 triangles, but the first post says not to post an image of it.

So, I'll just give a couple hints:



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Bombadil
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Schik wrote:
I found a solution that gives me 10 triangles, but the first post says not to post an image of it.

Very well done Schik, how many time did it take to you to find it? You can post an image if you want, it was because I thought it was impossible to post secret images.

Bombadil
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Sorry for the off-topic (again).

Doom wrote:
I mean a picture like the attached image. I've found 2 different solutions to it.

You mean this two?

Doom
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Yup. Those are the ones.

Hmm... Schik's hints made me only more confused...

Bombadil
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Here are my hints:

This one is pretty obvious:

I love this one (I don't know if I'll be able to write it):

Stefan
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Got it! Schik's hints are very helpful IMO.

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stigant
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Indeed! Well done Schick.

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agaricus5
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I shall join the list of congratulators of Schik. Your hints were quite helpful (and, if anyone still thinks this is some sort of conspiracy, then I assure you it is indeed possible).

Another hint that might help:



And (possibly spoilerish):



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Doom
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I can see it now... Agaricus's first hint was propably most helpful to me.

I had problems with Schik's hints, because I misunderstood one part of them... But man, I sure feel myself stupid now.

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[Last edited by Doom at 09-01-2005 04:54 PM]

stigant
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Update: At least one student in the geometry class I gave this problem to has solved it on her own. So kudos to her.

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