Tower of hanoi

In this medium-level challenge, you'll implement a Hanoi type that simulates the Tower of Hanoi puzzle, producing the complete sequence of moves needed to transfer all rings from one tower to another.

Detailed Explanation

type Hanoi<
  N extends number,
  From = 'A',
  To = 'B',
  Intermediate = 'C',
  Count extends unknown[] = []
> = Count['length'] extends N
  ? []
  : [
      ...Hanoi<N, From, Intermediate, To, [unknown, ...Count]>,
      [From, To],
      ...Hanoi<N, Intermediate, To, From, [unknown, ...Count]>,
    ]

How it works:

• This type implements the classic Tower of Hanoi recursive algorithm at the type level. The parameters represent the number of rings N, the source tower From, the destination tower To, and the auxiliary tower Intermediate.
• The Count tuple acts as a depth counter. Each recursive call adds one element to Count, effectively reducing the problem size by one ring at each level of recursion.
• When Count['length'] extends N (we have recursed N levels deep), we return an empty array as the base case -- there are no rings left to move.
• Otherwise, the solution follows three steps: first, recursively move the top N-1 rings from From to Intermediate (using To as the auxiliary). Then move the bottom ring directly from From to To as [From, To]. Finally, recursively move the N-1 rings from Intermediate to To (using From as the auxiliary).
• The spread operator ... concatenates all the move arrays together into a single flat sequence of [From, To] pairs.

This challenge helps you understand recursive type-level algorithms and tuple concatenation and how to apply these concepts in real-world scenarios.