Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.

Are you here to participate in a specific proposal? Click on the proposal tag (with the dark outline) to see only posts about that proposal and not all of the others that are in progress. Tags are at the bottom of each post.

Post History

66%

+2 −0

Incubator Q&A Draw the boundaries of the eight dominoes

Here's the image with a coordinate system for easier discussion. (I don't know how to straighten it out while I'm at it.) observations Position A1 is very constrained, so start there. We cann...

posted 1mo ago by Monica Cellio‭ · edited 1mo ago by trichoplax‭

Answer

#3: Post edited by

trichoplax‭ · 2026-08-06T14:55:27Z (about 1 month ago)
Add missing slash in closing details tag

Copy Link

Raw

Markdown

Here's the image with a coordinate system for easier discussion. (I don't know how to straighten it out while I'm at it.)
![rows A B C D, columns 1 2 3 4](https://proposals.codidact.com/uploads/y475ofvrz7tiwzl6wbloh8c8n630)
<details><summary>observations</summary>
Position A1 is very constrained, so start there. We cannot make the A1-B1 domino, because then any domino including A2 would be a duplicate and duplicates are not allowed. Therefore A1-A2 is a domino.
If we make A3-B3, then that would force A4-B4. That in turn would mean we would have to break up C2 and C3, which have many proximate duplicates. Let's pencil in A3-A4 instead. We might need to revisit based on other tiles.
B1-B2 and B3-B4 are unique and have no risk of overlaps, so we'll pencil those in.
We have to be careful of all those 2-pip and 3-pip cells near each other. We did not create A4-B4, so we are free to use C2-C3 (two 3-pip cells). If we do that, we can similarly do D2-D3, leaving C1-D1 and C4-D4.
Checksum: our eight dominos are: 0-0, 1-3, 1-1, 0-3, 3-3, 2-2, 2-1, 2-3.
</details>
<details><summary>or, drawn</summary>
(Yeah, without being able to straighten out the image I could only hand-draw these lines, so this is not elegant.)
![dominos outlined](https://proposals.codidact.com/uploads/a94kvqgwf775b0t1a12r2tq5w8bi)
~~<details>~~

Here's the image with a coordinate system for easier discussion. (I don't know how to straighten it out while I'm at it.)
![rows A B C D, columns 1 2 3 4](https://proposals.codidact.com/uploads/y475ofvrz7tiwzl6wbloh8c8n630)
<details><summary>observations</summary>
Position A1 is very constrained, so start there. We cannot make the A1-B1 domino, because then any domino including A2 would be a duplicate and duplicates are not allowed. Therefore A1-A2 is a domino.
If we make A3-B3, then that would force A4-B4. That in turn would mean we would have to break up C2 and C3, which have many proximate duplicates. Let's pencil in A3-A4 instead. We might need to revisit based on other tiles.
B1-B2 and B3-B4 are unique and have no risk of overlaps, so we'll pencil those in.
We have to be careful of all those 2-pip and 3-pip cells near each other. We did not create A4-B4, so we are free to use C2-C3 (two 3-pip cells). If we do that, we can similarly do D2-D3, leaving C1-D1 and C4-D4.
Checksum: our eight dominos are: 0-0, 1-3, 1-1, 0-3, 3-3, 2-2, 2-1, 2-3.
</details>
<details><summary>or, drawn</summary>
(Yeah, without being able to straighten out the image I could only hand-draw these lines, so this is not elegant.)
![dominos outlined](https://proposals.codidact.com/uploads/a94kvqgwf775b0t1a12r2tq5w8bi)
</details>

#2: Post edited by

Monica Cellio‭ · 2026-08-06T13:57:54Z (about 1 month ago)
corrected observations (no change in placements)

Copy Link

Raw

Markdown

Here's the image with a coordinate system for easier discussion. (I don't know how to straighten it out while I'm at it.)
![rows A B C D, columns 1 2 3 4](https://proposals.codidact.com/uploads/y475ofvrz7tiwzl6wbloh8c8n630)
<details><summary>observations</summary>
Position A1 is very constrained, so start there. We cannot make the A1-B1 domino, because then any domino including A2 would be a duplicate and duplicates are not allowed. Therefore A1-A2 is a domino.
Thus A3-B3 is not legal, so A3-A4 is a domino.
~~B1-B2 and B3-B4 are unique and have no risk of overlaps, so we'll pencil those in. We might need to revisit based on other tiles.~~
We have to be careful of all those 2-pip and 3-pip cells near each other. We did not create A4-B4, so we are free to use C2-C3 (two 3-pip cells). If we do that, we can similarly do D2-D3, leaving C1-D1 and C4-D4.
Checksum: our eight dominos are: 0-0, 1-3, 1-1, 0-3, 3-3, 2-2, 2-1, 2-3.
</details>
<details><summary>or, drawn</summary>
(Yeah, without being able to straighten out the image I could only hand-draw these lines, so this is not elegant.)
![dominos outlined](https://proposals.codidact.com/uploads/a94kvqgwf775b0t1a12r2tq5w8bi)
<details>

Here's the image with a coordinate system for easier discussion. (I don't know how to straighten it out while I'm at it.)
![rows A B C D, columns 1 2 3 4](https://proposals.codidact.com/uploads/y475ofvrz7tiwzl6wbloh8c8n630)
<details><summary>observations</summary>
Position A1 is very constrained, so start there. We cannot make the A1-B1 domino, because then any domino including A2 would be a duplicate and duplicates are not allowed. Therefore A1-A2 is a domino.
If we make A3-B3, then that would force A4-B4. That in turn would mean we would have to break up C2 and C3, which have many proximate duplicates. Let's pencil in A3-A4 instead. We might need to revisit based on other tiles.
B1-B2 and B3-B4 are unique and have no risk of overlaps, so we'll pencil those in.
We have to be careful of all those 2-pip and 3-pip cells near each other. We did not create A4-B4, so we are free to use C2-C3 (two 3-pip cells). If we do that, we can similarly do D2-D3, leaving C1-D1 and C4-D4.
Checksum: our eight dominos are: 0-0, 1-3, 1-1, 0-3, 3-3, 2-2, 2-1, 2-3.
</details>
<details><summary>or, drawn</summary>
(Yeah, without being able to straighten out the image I could only hand-draw these lines, so this is not elegant.)
![dominos outlined](https://proposals.codidact.com/uploads/a94kvqgwf775b0t1a12r2tq5w8bi)
<details>

#1: Initial revision by

Monica Cellio‭ · 2026-08-06T04:02:20Z (about 1 month ago)

Copy Link

Raw

Markdown

Here's the image with a coordinate system for easier discussion.  (I don't know how to straighten it out while I'm at it.)

![rows A B C D, columns 1 2 3 4](https://proposals.codidact.com/uploads/y475ofvrz7tiwzl6wbloh8c8n630)

<details><summary>observations</summary>

Position A1 is very constrained, so start there.  We cannot make the A1-B1 domino, because then any domino including A2 would be a duplicate and duplicates are not allowed.  Therefore A1-A2 is a domino.

Thus A3-B3 is not legal, so A3-A4 is a domino.

B1-B2 and B3-B4 are unique and have no risk of overlaps, so we'll pencil those in.  We might need to revisit based on other tiles.

We have to be careful of all those 2-pip and 3-pip cells near each other.  We did not create A4-B4, so we are free to use C2-C3 (two 3-pip cells).  If we do that, we can similarly do D2-D3, leaving C1-D1 and C4-D4.

Checksum: our eight dominos are: 0-0, 1-3, 1-1, 0-3, 3-3, 2-2, 2-1, 2-3.

</details>

<details><summary>or, drawn</summary>

(Yeah, without being able to straighten out the image I could only hand-draw these lines, so this is not elegant.)

![dominos outlined](https://proposals.codidact.com/uploads/a94kvqgwf775b0t1a12r2tq5w8bi)

<details>

Communities

Post History