A Sudoshiki puzzle here is assumed to be a Futoshiki puzzle on a standard Sudoku grid (eg: 9 3x3 regions, 8 2x4 regions, 6 2x3 regions, etc).

Since clues can be in two forms - givens and relationships - a puzzle has 3 basic attributes:

- N - the grid size
- G - the number of givens
- R - the number of relationship clues (<, >)

A puzzle, FP(N, G, R) or SI(N, G, R) (SI for Sudoshiki, aka Sudoku Inequality) is minimal if removal of any given or relationship causes the puzzle to have multiple solutions.

My primary interest is in puzzles with G = 0, but I will in time take a look at puzzles with G > 0.

Searching for minimal cases is a time-consuming business, so my results for N > 5 are by no means definitive, but here they are:

- Code: Select all
`Minimal Futoshiki/Sudoshiki (no givens)`

N R(FP) R(SI)

-----------------------

4 4 3

5 6

6 9 8

7 15

8 24 19

9 36 27

If anybody is aware of any examples of smaller R I'd be glad to hear from you, of course!