Advanced Tiling Puzzle

Geometry Level 2

Tile Carpets is a new carpet company that prides itself on selling individual carpet tiles that can be laid down side by side to form a single solid plane.

They have received some constructive feedback from their customers, who feel that the current selection of tiles are too typical and boring. In response, Tile Carpets is designing a more interesting tile shape, which can still be laid down side by side to form a single solid plane, with no gaps between the tiles.

Which of the following tiles satisfy this criteria?

Image credit: Wikipedia

1 2 3 4

2 solutions

Tong Choo
Jan 16, 2014

I chose 4. But I don't see why 2 isn't also another answer.

Why do you think $2$ fits?

Michael Tong - 7 years, 4 months ago

You can fit the H shapes together in slanted rows. http://nrich.maths.org/content/id/4976/jelena.gif

Tong Choo - 7 years, 4 months ago

Ah, I didn't think of that. I was thinking that there were too many protruding parts, and too few 'interior' parts.

This is a badly set question then.

Calvin Lin Staff - 7 years, 4 months ago

@Calvin Lin – So actually both 2 and 4 is correct? (I chose 2)

Vincent Tandya - 7 years, 4 months ago

@Calvin Lin – Is there any way both answers could be marked correct? I think that might also be a good feature (something like check all that are true).

Daniel Chiu - 7 years, 4 months ago

@Daniel Chiu – Not right now. That would get very confusing to explain and differentiate.

I've updated the question, which would hopefully fix it.

Calvin Lin Staff - 7 years, 4 months ago

Yes, that's what I did too -- excepting the coloring pattern. I would have colored connecting pieces the same. :)

Peter Byers - 7 years, 4 months ago

The interior angles are divisible by 360.

Chandler West - 7 years, 4 months ago

Yeah I put 2...

Daniel Chiu - 7 years, 4 months ago

Same here.. I was stuck between 2 and 4 and chose 2 :(

Aditya Pappula - 7 years, 4 months ago

i chose 2 :(

Antonio Valente Macarilay - 7 years, 4 months ago

i chose 4 as tiles can easily fit in them without any gap. It is clear from the angle given

Dipendra Singh Mal - 7 years, 4 months ago

You can do the same with 2.

Tong Choo - 7 years, 4 months ago

I chose 2, but it's wrong...No matter what, I strongly agree that 2 is the correct answer, this is because the lines which form the angle $104^{\circ}$ is longer than the lines which form the angle $256^{\circ}$ , so obviously it will form a gap, therefore I don't know how are you going to tile $4$ without a gap. :\

敬全钟 - 7 years, 4 months ago

4 and 2 are both answers. For 4, you stack to form a column pointing up, and then to the side, you stack and form another column pointing down, and alternate columns like that.

Tong Choo - 7 years, 4 months ago

Chethan Kumar - 7 years, 3 months ago

i wrote 2 :( lost points! :(:(

Shreya R - 7 years, 2 months ago

Sally Allam
Jan 19, 2014

Bees are intelligent for their cells' choice (❀◕‿◕)..... A regular hexagon. Good choice, bees ッ

1 and 2, can't make complete cells, if you think about it.

3 and 4, you have to get their unknown angles.

3 has an outside obtuse angle which is 140 degrees. This make it hard to include a similar shape here..... 4 has an outside obtuse angle which is 104 degrees. This make it easy to include a similar shape here.

Here are some photos to explain:

https://www.facebook.com/photo.php?fbid=641602379211987&set=a.641601732545385.1073741827.100000866920568&type=1&permPage=1

https://www.facebook.com/photo.php?fbid=641586399213585&set=a.641601732545385.1073741827.100000866920568&type=1&relevant_count=1

Sally Allam - 7 years, 4 months ago

This is how 2 will look, if we make it cells.

https://www.facebook.com/photo.php?fbid=642008365838055&set=a.641601732545385.1073741827.100000866920568&type=1&relevant_count=1

there will be gaps.

Sally Allam - 7 years, 4 months ago

Advanced Tiling Puzzle

Image credit: Wikipedia

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