holt >> 週四 十二月 8 - 11:25

Courtesy Numpty:

• Can you cut up an equilateral triangle and rearrange its parts to get a square?

Numpty >> 週四 十二月 8 - 19:26

I've just seen this. 

The simple answer is, of course, yes. In principle you can cut up any triangle and form a square with the parts. The question is where do you make the cut(s)? 

I'll have to give it some thought ... 

Numpty >> 週四 十二月 8 - 23:22

I've given it some thought and maybe have 'half a solution'. :)

I calculated the area of an equilateral triangle of unit length (=1) as √3/4 square units.  [The height is √3/2 (Pythagoras), so the area is √3/4.] 

The area of the square must be the same, so the length of the 2 sides of the square must be 4√3/2 [4th root].

Half the height of the triangle is √3/4, So the square root of half the height, will give us 4√3/2, which is the length of one side of the square. Once we've got that then we can cut everything to fit. 

I then went down a bit of a rabbit warren trying to work out how to construct that, perhaps using a compass. I'm sure it's possible but don't have the urge to spend any more time on it. 

How close did I get?

holt >> 週五 十二月 9 - 13:48

You've got the gist of it, but the devil (or should I say the joy?) lies in the details so maybe you should give it a go.

This is the theorem if you're interested in it, there was an animation of this online but it seems to slip my mind: https://en.wikipedia.org/wiki/Wallace%E2%80%93Bolyai%E2%80%93Gerwien_theorem

Another one:

• Can you cut a square into an odd number of triangles of equal area?

(You can tell me which topic you're interested in as well, I should have something related to it)

Numpty >> 週五 十二月 9 - 16:01

I don't really mind which topic. I think it has to be generally suitable so that anyone can have a go at them.

If I get stuck can I ask the kids to do my homework? :D

holt >> 週六 十二月 10 - 04:27

Lol sure, take all the help you need.

The question about the square is especially enticing.

Numpty >> 週六 十二月 10 - 14:59, 新編輯 週六 十二月 10 - 15:26

Do you have your own solution to these puzzles or are they ones you haven't done yourself? 

The first one you haven't given a solution exactly where to cut the triangle.  The wiki page you posted gives a general diagram but not the precise points where it needs to be cut.

The second one, I give up. Not entirely sure if it's even possible. 

holt >> 週日 十二月 11 - 05:40

Do you want me to post the solutions here?

Numpty >> 週日 十二月 11 - 11:15

Yes, I think any questions or puzzles have to be answered at some point by the originator. 

But you decide when. I would suggest giving a rough timescale for anyone wanting to have a go before posting the solution. 

One thing I would bear in mind with future puzzles is that solutions potentially involving a diagram - or anything else that can't easily be posted in a thread - is going to be more difficult to give clear answers.

holt >> 週六 十二月 17 - 19:54

It would be nice to see others participate as well

Numpty >> 週六 十二月 17 - 20:01

I suspect the thread title is rather off-putting for most people. 

Maybe frame it in a different way. 'Brain teasers' 'Logic Puzzles' or something similar. 

holt >> 週五 十二月 30 - 12:58

A bat and a ball together cost 1.10$. The bat costs a dollar more than the ball. How much does the bat and the ball cost?

This is an attempt to gauge participation.

Numpty >> 週五 十二月 30 - 13:18

That reminds me of the old aeroplane riddle. A plane crashed on the border of 3 different countries, Germany, France and Switzerland. Where did they bury the survivors? 

Lee >> 週六 十二月 31 - 23:51

You don't bury survivors.