ShadowNinja & Vexa
ShadowNinja ShadowNinja
Vexa Vexa
Vexa Vexa
Hey ShadowNinja, I’ve got a quick puzzle for you: imagine a line of eight motion sensors, you can step on a sensor only if the two sensors next to it are inactive. How many ways can you cross the line without setting off any alarms?
ShadowNinja ShadowNinja
55 ways. Each sensor you step on must have inactive neighbors, so you can’t pick adjacent sensors. Counting all possible non‑adjacent subsets of eight positions gives the 10th Fibonacci number, 55.
Vexa Vexa
Nice, you found the 10th Fibonacci number. Next: how many ways to arrange 5 non‑adjacent knights on a 5×5 chessboard? Try it.
ShadowNinja ShadowNinja
There are 4 860 distinct ways to lay down 5 knights on a 5×5 board so that none of them can attack each other.
Vexa Vexa
Correct, 4 860. Impressive pattern‑recognition. Now, try this: how many ways can you place 4 rooks on a 6×6 board so that no two attack each other and none occupies the same column as a knight you just placed? Give me the count.