青春のようなhttps://youtu.be/pGWrTC53z6A
(This was discussed on r/math and Hacker News.) In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I hope to go further and explain h
In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an $n \times n \times n$ Rubik's Cube with missing stickers is NP-complete. We prove this result first for the simpler case of the Rubik's Square---an $n \times n \times 1$
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