Marc Leonard Overbeck

A proof candidate for 17 squares: the 1998 packing cannot be beaten. s(17) = 4.67553009…

Built with @OpenAI Codex and @AnthropicAI Claude. Thanks to @ojoshe, @_Mira___Mira_, @guzhou0806 and @ManassehA06, whose work this builds on.

Try to break it: github.com/Kleddamag/the-…

1/2
I used Codex (@ChatGPT) to push the lower bound for packing 17 unit squares from 4.619791… in my last post to 4.66001.
That closes 72.16% of the gap that was left. Including my earlier progress: 74.71% since the Mira/Guzhou bound.
The exact minimum is still open.

1/2

Me + Codex (@ChatGPT) pushed the lower bound for packing 11 unit squares into a square from 3.826447… to 3.875.

That closes 95.89% of the gap to the best known packing (3.87708359…).

Rotations allowed. Exact minimum still open.

17 unit squares. how small can the outer square be?

Me + Codex (@ChatGPT) pushed the lower bound:

4.61415354 → 4.61979109

That closes 9.19% of the remaining gap to the known packing at 4.67553009.

Still unsolved. The community's been moving fast ↓