Post #2672389
2026-01-22 18:04 UTC
And here's one of the big flourishes: if we know we have solutions for n=5 and n=6, and we know we can make solutions for n=5+3k and n=6+4j, we can make solutions for ALL values of n>=8.
Proof? n=5, do the +3 rectangle split trick and we have an n=8 solution.
n=6, do the +3 split trick and we have n=9.
n=6, do the +4 rectangle wraparound trick, we have n=10.
Now we know we have solutions for 8, 9, and 10. And we can get +3 solutions for each: 11, 12, 13, and then 14, 15, 16, and then...
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 18:07
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.