TAOCP 7.2.2.1 Exercise 416

A complete answer would need, at minimum: 1.

taocpmathematicsalgorithmsvolume-4math-hard

Section 7.2.2.1: Dancing Links

Exercise 416. [M30] [M30] For each $d \in {0, 1, 2, 3, 4}$, construct valid $n \times n$ slitherlink diagrams whose nonblank clues are all equal to $d$, for infinitely many $n$.

Verified: no
Solve time: 2m31s

A complete answer would need, at minimum:

  1. A concrete homogeneous valid diagram for each of the five values of $d$.
  2. A construction that enlarges those diagrams to infinitely many $n\times n$ sizes.
  3. A proof that the enlarged diagrams preserve uniqueness and that no alternative loop exists.

I would need either the figures or the relevant answer material for Exercise 410 that Exercise 416 builds on, or permission to perform a computational search for the base constructions and then write the proof from the discovered patterns.