arithmetic – The Royal Relay on a Chessfield

Playable Model

Within the historical Kingdom of Gridoria, a mysterious curse has frozen the whole realm: each citizen, each fortress, each mountain.

The royal courtroom’s solely hope lies in a sacred Relay Ritual, handed down by way of generations: a ceremony the place every noble chess piece should transfer in strict succession, one after one other, throughout the whole land: the 8×8 Chessfield. If they can not go to all squares, they fail.

However the ritual should be completely coordinated. No sq. could also be stepped on twice, and the royal items should comply with their preordained order, handing over the mission like a sacred baton.

The Sacred Sequence:

Each bit should transfer on this actual order, repeating endlessly:

👑 King → ♝ Bishop → ♙ Pawn → ♜ Rook → ♞ Knight → ♛ Queen → repeat...

Problem

Devise a traversal that visits the utmost variety of distinctive squares on an 8×8 chessboard underneath the next guidelines:

1. You could begin with the King on any sq. you need.

2. You then transfer in response to this fastened repeating cycle:

   King → Bishop → Pawn → Rook → Knight → Queen → King → ...
   

3. Every transfer:

   • Should comply with the usual motion guidelines of that piece.
   • Should begin from the sq. you simply landed on.
   • Should go to a sq. not but visited.

Essential Guidelines

• You can not go to the identical sq. twice, together with any sq. handed over throughout a slide (for Bishop, Rook, and Queen).
• Sliding items (♝, ♜, ♛) occupy each sq. they cross by way of, and all are marked as visited.
• The Pawn can solely transfer one sq. ahead, and this ahead course is fastened globally earlier than the journey begins (assume “North” = upward).
• The Knight (♞) “jumps” over squares, and solely its touchdown sq. counts.

You possibly can select:

• Any beginning sq..
• However you need to at all times start with the King, and comply with the order strictly.

Targets

• Major Goal: What’s the most variety of distinctive squares that may be visited on this strict royal relay utilizing the fewest attainable piece turns? Will the sacred sequence be sufficient to cleanse the realm, or will the curse stay unbroken?

• Secondary Goal: What’s the most variety of particular person piece turns (i.e., strikes) you may execute earlier than getting caught?

Playable Model

Notice: The query is totally my unique work. I used a big language mannequin solely to refine the English and enhance formatting.