IBM Research

PUZZLE   IBM-255

Large- and small-area knight's cycles

IBM Research · Ponder This · 2019-07

IBM Ponder This #255 · July 2019

This month's challenge is by Hugo Pfoertner. (Thanks!)

A non-intersecting knight's cycle is a closed tour made of legal moves of a chess knight on a rectangular board of size mXn, such that the straight lines connecting consecutively visited fields make a simple polygon of an enclosed area A.
Find two non-intersecting knight's cycles of length 14 on boards of size 40 such that the difference between their areas is at least 7.

As an example, there are two non-intersecting knight's cycles of length 4 on boards of size 16 such that the difference between their areas is 1:
The first has an area of 3 on 4x4 board: a1 c2 d4 b3 a1
and the second has an area of 4 on 3x5 board: c1 e2 c3 a2 c1.

Submit your solution as two lines of 15 visited fields (start=end) using algebraic chess notation as we used above.

Solution

Best opened after a real attempt

To be added.