Thread

Tweet 1

@moultano All this discussion of bishops made me realize the obvious generalization of rooks is also wrong. Bishops should be able to move along the span of any vector of 1,0,-1 with entries summing to 0 mod 2 and the rook with those summing to 1 mod 2

---

Tweet 2

@moultano Then the queen moves like both and the knight moves to every square less than distance 2 away with sup norm that the queen doesn't move to

---

Tweet 3

@moultano Now I'm not super confident you can't always check mate since the knight covers exponentially much of the length 2 cube. But maybe nothing can cover the missed squares efficiently. Probably it's still impossible at relatively low dimension

---