Post #2672390
2026-01-22 18:07 UTC
So! To finish summing up what the video covers:
We know we have no solution for n=1, 3, and 4.
We know we DO have solutions for n=5, 6, and every number from 8 up to infinity.
We haven't shown a solution for n=7 yet. Is there one? There sure is! In fact, there are multiple; I paused the video, worked one out, felt pleased that I'd found The Solution, and resumed and found out they'd solved it a different way! Here's mine on the left and theirs on the right.
Replies (3)
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@joshmillard@mastodon.social 2026-01-22 18:26
So that's the preamble. Fun video, neat idea, and they specifically did not get into a related, stickier question that I am now thinking about: how *many* distinct ways can you create a solution for any given n? Let's not just find *A* solution, let's find as many as we can, and try to think about HOW to look for them. So what counts as distinct? Let's ignore orientation: two vertical rectangles vs. two horizontal rectangles is really just the same thing rotated.
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@operand@todon.nl 2026-01-22 18:25
@joshmillard@mastodon.social wait, isn't the right solution here n=6?
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@middleclasstool@phire.place 2026-01-22 19:29
@joshmillard@mastodon.social am I counting wrong, or is the one on the right just six?