Is the Original Figure Considered a Shape in This Puzzle?

[jjs789]

Draw a picture showing four identical shapes where each shape has at least one border with the other three. Your picture should be a single two-dimensional shape containing no gaps or holes.

Tried many shape combinations irregular and regular. We got given a hint of not to think or draw shapes because you will not get the answer. Now even more confused.

 

[Dickfore]

If you have 4 figures and 3 of them have one common side with a central figure, how many sides does the central figure have to have? Since the figures are identical, the other ones would have the same number of sides. How would you arrange them?

EDIT:

I just saw that every figure has to have a common side with ALL the other ones. I believe this is impossible on a plane, but I cannot prove it right now.

 

[jjs789]

The shapes have to be the same size cannot be scaled, but they can be rotated. We think its probably an irregular shape but still no success so far

 

[berkeman]

The shapes have to be the same size cannot be scaled, but they can be rotated. We think its probably an irregular shape but still no success so far

Hint -- use technology to help you solve this. Google the first few words of your post, and look through the first few hits...

Pretty clever solution, actually. I don't think I would have figured it out without Google. BTW, you should probably attribute Google when you hand in your solution...

 

[zgozvrm]

I'd love to see the answer to this. I've gone through what seems like reams of paper trying to come up with a solution. I finally "gave in" and consulted the all-mighty Google, but to no avail. I can find very few answers, all of which are incorrect. Can you post a link, or perhaps send it to me via IM?

 

[berkeman]

I'd love to see the answer to this. I've gone through what seems like reams of paper trying to come up with a solution. I finally "gave in" and consulted the all-mighty Google, but to no avail. I can find very few answers, all of which are incorrect. Can you post a link, or perhaps send it to me via IM?

Hmm. I went back to the one that I thought solved the question, and it does turn out to be incorrect. Figure 2 under Geometry here:

http://members.cox.net/mathmistakes/puzzles.htm

The inverted 4th figure is what I though was clever, but the end pieces do not share a border. Will try Google some more...

 

[berkeman]

I'd love to see the answer to this. I've gone through what seems like reams of paper trying to come up with a solution. I finally "gave in" and consulted the all-mighty Google, but to no avail. I can find very few answers, all of which are incorrect. Can you post a link, or perhaps send it to me via IM?

I think I might be close. I'll PM you my idea...

 

[willem2]

A sets of shapes on this page: http://karl.kiwi.gen.nz/prtetrad.html"

a bit below the middle of the page, is the best I could find on the internet.
It's nearly convex. Wether a convex shape is possible seems to be an open problem

 

[zgozvrm]

A sets of shapes on this page: http://karl.kiwi.gen.nz/prtetrad.html"

a bit below the middle of the page, is the best I could find on the internet.
It's nearly convex. Wether a convex shape is possible seems to be an open problem

Wow! I was pretty close to getting the figure at the top of the page! I didn't think there'd be so many possibilities, although I figured there were bound to be a few.

Many are slight variations on each other.

 

[zgozvrm]

In addition, many have flipped pieces; I was trying to solve by only rotating them (which is the more elegant solution, in my opinion).

 

[Dick]

I think I might be close. I'll PM you my idea...

This all really depends on what the exact definition of 'shape' is. Picture a square with a triangle sharing a vertex with the square sticking out of a corner. Now cut out a hole in the square corresponding to the triangle and glue four of them together. Is the original figure a 'shape'?