Surely they can fit?Find a heptagon with mirror symmetry that can tile a flat planeMax 4x1 pattern fit within 11x11 areaFit as many overlapping generators as possible
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Surely they can fit?
Find a heptagon with mirror symmetry that can tile a flat planeMax 4x1 pattern fit within 11x11 areaFit as many overlapping generators as possible
$begingroup$
Suppose you have a grid of squares that has even dimensions, with at least one dimension greater than or equal to 4 squares, and from one corner you remove a 1x4 rectangle of those squares
for example:
□□□□□□
□□□□□□
□□□□□□
XXXX□□
Can you fill in that grid using as many copies of the following shapes as you like?
(Each shape can be rotated any of the four ways, and can be flipped/mirrored)
□□
□□
□□
□□
□□□□
□□□□
If you can, provide an example solution. If you cannot, then you should provide a reasonable argument to why it can't be done.
tiling
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
$endgroup$
add a comment |
$begingroup$
Suppose you have a grid of squares that has even dimensions, with at least one dimension greater than or equal to 4 squares, and from one corner you remove a 1x4 rectangle of those squares
for example:
□□□□□□
□□□□□□
□□□□□□
XXXX□□
Can you fill in that grid using as many copies of the following shapes as you like?
(Each shape can be rotated any of the four ways, and can be flipped/mirrored)
□□
□□
□□
□□
□□□□
□□□□
If you can, provide an example solution. If you cannot, then you should provide a reasonable argument to why it can't be done.
tiling
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
$endgroup$
add a comment |
$begingroup$
Suppose you have a grid of squares that has even dimensions, with at least one dimension greater than or equal to 4 squares, and from one corner you remove a 1x4 rectangle of those squares
for example:
□□□□□□
□□□□□□
□□□□□□
XXXX□□
Can you fill in that grid using as many copies of the following shapes as you like?
(Each shape can be rotated any of the four ways, and can be flipped/mirrored)
□□
□□
□□
□□
□□□□
□□□□
If you can, provide an example solution. If you cannot, then you should provide a reasonable argument to why it can't be done.
tiling
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
$endgroup$
Suppose you have a grid of squares that has even dimensions, with at least one dimension greater than or equal to 4 squares, and from one corner you remove a 1x4 rectangle of those squares
for example:
□□□□□□
□□□□□□
□□□□□□
XXXX□□
Can you fill in that grid using as many copies of the following shapes as you like?
(Each shape can be rotated any of the four ways, and can be flipped/mirrored)
□□
□□
□□
□□
□□□□
□□□□
If you can, provide an example solution. If you cannot, then you should provide a reasonable argument to why it can't be done.
tiling
tiling
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
asked May 11 at 23:50
micsthepickmicsthepick
2,52311128
2,52311128
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No, you cannot:
Color the grid like this.
Since the grid (before removal of the four cells) has even dimensions, it is made up of 2x2 blocks with each color once. So each color appears the same number of times.
All of the given shapes will always cover the same number of squares of each color: the first two cover one of each, and the last covers two of each. But after marking off the unused cells, the grid has more red and blue cells than yellow and green. So you can't cover the grid perfectly.
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
$endgroup$
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
No, you cannot:
Color the grid like this.
Since the grid (before removal of the four cells) has even dimensions, it is made up of 2x2 blocks with each color once. So each color appears the same number of times.
All of the given shapes will always cover the same number of squares of each color: the first two cover one of each, and the last covers two of each. But after marking off the unused cells, the grid has more red and blue cells than yellow and green. So you can't cover the grid perfectly.
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
$endgroup$
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
add a comment |
$begingroup$
No, you cannot:
Color the grid like this.
Since the grid (before removal of the four cells) has even dimensions, it is made up of 2x2 blocks with each color once. So each color appears the same number of times.
All of the given shapes will always cover the same number of squares of each color: the first two cover one of each, and the last covers two of each. But after marking off the unused cells, the grid has more red and blue cells than yellow and green. So you can't cover the grid perfectly.
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
$endgroup$
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
add a comment |
$begingroup$
No, you cannot:
Color the grid like this.
Since the grid (before removal of the four cells) has even dimensions, it is made up of 2x2 blocks with each color once. So each color appears the same number of times.
All of the given shapes will always cover the same number of squares of each color: the first two cover one of each, and the last covers two of each. But after marking off the unused cells, the grid has more red and blue cells than yellow and green. So you can't cover the grid perfectly.
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
$endgroup$
No, you cannot:
Color the grid like this.
Since the grid (before removal of the four cells) has even dimensions, it is made up of 2x2 blocks with each color once. So each color appears the same number of times.
All of the given shapes will always cover the same number of squares of each color: the first two cover one of each, and the last covers two of each. But after marking off the unused cells, the grid has more red and blue cells than yellow and green. So you can't cover the grid perfectly.
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
answered May 12 at 1:42
Deusovi♦Deusovi
65k6223282
65k6223282
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
add a comment |
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
that’s pretty much my reasoning!
$endgroup$
– micsthepick
May 12 at 1:55
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
$begingroup$
Danf Deus actually gave an answer! For the first time in forever Okay in all seriousness, this is pretty amazing. Also the first post by micsthepicks I've seenin a while. Good to see you again @micsthepick
$endgroup$
– North
May 12 at 5:03
add a comment |
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