Trace Elements

A19327

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Feb 19, 2023
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Within the boundaries of the shape, draw the outlines of the six figures described. Do this by following the lines formed by the tiles within the shape. The figures you draw may be odd shapes -- for example, a 6-sided figure doesn't have to be a typical hexagon shape. When you've finished, the six figures should fill the large shape exactly; they may not overlap each other or fall outside the boundaries of the shape. We've started you off by showing where Figure #5 is located.

1.) A 4-sided figure that encloses 8 triangles. It has more triangles in the top row than any other figure.

2.) A 6-sided figure that encloses 10 triangles.

3.) A 6-sided figure that encloses 6 triangles. It has more triangles in the bottom row than any other figure.

4.) A 5-sided figure that encloses 5 triangles.

5.) A 6-sided figure that encloses 6 triangles.

6.( A 4-sided figure that encloses 7 triangles. It has more triangles in more rows, including two in the bottom row, than any other figure.


1738101462375.png
 
Within the boundaries of the shape, draw the outlines of the six figures described. Do this by following the lines formed by the tiles within the shape. The figures you draw may be odd shapes -- for example, a 6-sided figure doesn't have to be a typical hexagon shape. When you've finished, the six figures should fill the large shape exactly; they may not overlap each other or fall outside the boundaries of the shape. We've started you off by showing where Figure #5 is located.

1.) A 4-sided figure that encloses 8 triangles. It has more triangles in the top row than any other figure.

2.) A 6-sided figure that encloses 10 triangles.

3.) A 6-sided figure that encloses 6 triangles. It has more triangles in the bottom row than any other figure.

4.) A 5-sided figure that encloses 5 triangles.

5.) A 6-sided figure that encloses 6 triangles.

6.( A 4-sided figure that encloses 7 triangles. It has more triangles in more rows, including two in the bottom row, than any other figure.


View attachment 39086
It's a nice puzzle (though not exactly advanced math).

Where do you need help? Please show us what you have tried, so we can see what to suggest.
 
It's a nice puzzle (though not exactly advanced math).

Where do you need help? Please show us what you have tried, so we can see what to suggest.
Sure. I cant show you but I can explain it to you. I didnt want to confuse anyone by putting my part in bc I am unsure of it, using pencil. It makes it harder to view the image when you have in pencil your own part. Anyway, there are two that I am pretty sure of but unsure of how they lie. Clues #3 and #6 state they have a portion on the bottom row, with #3 being the bigger portion. However, they can go 2 different ways and thats where I am stuck. #6 can look like an upside down parallelogram coming down the left , like a diagonal line. However, it can go on the other side as well, they are interchangable. Its what is needed to do beyond that where I need some help. I would appreciate it.
 
Okay, that's pretty much where I started, too. You need to be able to try things and back them out if they don't work out. Here is one version of what you've said:
1.) A 4-sided figure that encloses 8 triangles. It has more triangles in the top row than any other figure.

2.) A 6-sided figure that encloses 10 triangles.

3.) A 6-sided figure that encloses 6 triangles. It has more triangles in the bottom row than any other figure.

4.) A 5-sided figure that encloses 5 triangles.

5.) A 6-sided figure that encloses 6 triangles.

6.( A 4-sided figure that encloses 7 triangles. It has more triangles in more rows, including two in the bottom row, than any other figure.
1738119659162.png
There are 23 triangles left; the three last pieces will use them up, and #1 is the obvious next one to focus on. I made one try, which failed when the last piece needed 7 sides rather than 6. So we take off a piece or two and try something else. If necessary, we swap pieces 3 and 6 and start over.

I think the hardest part may be to find a medium in which you can keep tracks of tries; maybe use tracing paper on top of the picture, or use a good drawing program. (I used a cheap one!) But part of the work can be in your head, as you imagine possibilities.
 
Okay, that's pretty much where I started, too. You need to be able to try things and back them out if they don't work out. Here is one version of what you've said:

View attachment 39087
There are 23 triangles left; the three last pieces will use them up, and #1 is the obvious next one to focus on. I made one try, which failed when the last piece needed 7 sides rather than 6. So we take off a piece or two and try something else. If necessary, we swap pieces 3 and 6 and start over.

I think the hardest part may be to find a medium in which you can keep tracks of tries; maybe use tracing paper on top of the picture, or use a good drawing program. (I used a cheap one!) But part of the work can be in your head, as you imagine possibilities.
So you did the exact same steps as I did. The problem I ran into was the only place to put #1 messed up the steps avail with the open spaces to fit the remaining ones. So thats where I get stuck. It seems impossible. Dont be coy. Please tell me anything that you have figured out about this I have been stuck on it for a couple of days and just want to get done with it.
 
Dont be coy. Please tell me anything that you have figured out about this I have been stuck on it for a couple of days and just want to get done with it.
I'm not being "coy"; I'm following the rules of the site, which means to HELP you, not to do it FOR you. I'm offended by your assumption!

I showed you everything I've done, except for the failed try that you describe:
FMH139289 filling in shapes.png

I'm not so interested in the problem that I would finish solving it without giving you a chance. But I told you what I would do next if I cared: having given up on continuing from what I showed you, I'd swap the locations of 3 and 6. If that didn't work, I'd ask the originator of the problem to confirm the problem was stated correctly (and that you copied it correctly).

Where did it come from, and why does it matter so much to you?
 
I was being playful, lighthearted about it. Coy isnt an insult anyway. This isnt a homework assignment, its from a crossword puzzle book. To be perfectly honest, its probably bc Im on the spectrum. Most people would skip it and move on and I dont work that way. I cant move on until I finish it. By the way, you did it like I did but there is one problem, whch I also ran into. Look at the yellow one, its too many sides.
 
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