Re: Minimum number of clues for 2x4 Sudokus

Afmob — Tue Feb 14, 2012 8:56 am

Author: Afmob

Posted: Tue Feb 14, 2012 8:56 am

I calculated all essentially different, uniquely solvable 2x4 Sudokus with 14 clues and my initial guess of over 100,000 puzzles was way off.

There are only 8,280 essentially different puzzles which come from 6,600 essentially different solution grids. Note that the total number of solution grids is 1,673,187 (as calculated here).

Minimum number of clues for 2x4 Sudokus

Afmob — Wed Nov 02, 2011 4:40 pm

Author: Afmob

Posted: Wed Nov 02, 2011 4:40 pm

This is a continuation of the following thread.

I have proven that a 2x4 Sudoku needs at least 14 given clues to be uniquely solvable. I've done this by examining all essentially different patterns and their essentially different Sudokus regarding automorphisms.

There are 32,597,396 essentially different patterns (excluding ones with more than one free row or column per band) with one pattern having up to 2.5 million different puzzles.
Since I haven't tested all patterns in one batch, I will calculate the total number of Sudokus being tested over the weekend.

Edit: The calculation was completed and the total number of Sudokus being tested is about 15.966 trillion (1.5966 * 10^13), so a pattern has an average of 490,000 essentially different Sudokus.

Sudoku Programmers

Re: Minimum number of clues for 2x4 Sudokus

Minimum number of clues for 2x4 Sudokus