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We were surprised that the unassembled area didn't depend on the number of puzzle pieces. The intuition is this: if you have a small number of large pieces, the gaps between pieces are big, but this is multiplied by a small total number of pieces, and vice versa for small pieces.

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So there you have it: you'll need a puzzle table just under twice as big as your assembled puzzle in order to not resort to the box lid or that random side table. Grab a puzzle and impress your relatives this holiday season with your predictive powers!

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Interesting Nature paper from Google DeepMind on using LLMs for solving mathematical problems that are easy to evaluate but difficult to solve:

nature.com/articles/s41586-023

Their procedure, which they call FunSearch, applies an islands model genetic algorithm using the Codey LLM on the cap set problem and online bin packing.

This seems in line with my personal theory that we should view LLMs similarly to MCMC methods, i.e., they are closer to random number generators and should be optimized for sampling.

@highergeometer @monsoon0 I second emphasizing the history and progressive nature of math. Here's a wonderful quotation from Alfred North Whitehead's 'An Introduction to Mathematics'
gutenberg.org/ebooks/41568

Was doing a joke about a modern Jacob and Esau but I think the reference is too obscure?

@peterluschny What I meant by mathematical programming was optimization (en.m.wikipedia.org/wiki/Mathem). However, I think you're right that the quote is referring to computer programming. I believe this is the letter that contains this quote, in which Dijkstra clearly is referring to computer programming:

cs.utexas.edu/users/EWD/transc

who called it "legend of zelda speedrunning" and not "link-time optimization"

@peterluschny Programming in this context is mathematical programming, not computer programming, correct?

#Django is the Superman framework

1. Comes from a small town in Kansas
2. First job was for a newspaper
3. Works for a perfectionist boss with a perpetual deadline

Love his William Holman Hunt allegorical painting for Turing's 1936 paper in which he invents the universal computer, which runs on a single infinitely long piece of tape. I believe the two figures bowing at his feet are the muses of logic and engineering.

Here are four ways I’ve found to solve an nxnxn cube to embed a trefoil knot. Five layers is the smallest cube I’ve been able to put this knot on. On a 9cube, I’ve found solutions that use 2 colors of thread, 2 faces, and a solution that leaves the reverse side solved as solid colors.

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