Puzzle Description:

In this puzzle, there are no overlapping colors in any of the rows, columns, or 45° diagonals.

#1: Joe (infrapinklizzard) on Mar 22, 2014 [SPOILER]

I decided to play with the concept in #6435: "32 Queens" http://webpbn.com/6435 and especially in its comment #7. Specifically, I decided to see what would happen if you applied a "no diagonal" rule while also adding that ALL squares must be covered by a queen.

This has rotational symmetry, with each of four colors making a chair-like shape with its "back" going into a corner. (E.g. the red chair is leaning back against the right wall.) The fifth color (white) makes a five-pip shape.

I'm pretty sure there is no way to have each square be covered by a queen and fulfill the requirements above without it being symmetrical.

I also think that you cannot have all squares covered by queens and fulfill the above requirements while having a board that has dimensions that do not have a prime factor >2 (eg. 2x2, 4x4, 8x8 etc; but 6x6 would work as it has a prime factor of 3).

And I have found a 6x6 that works. It has rotational symmetry. Four colors have one pattern and two another.

I'm not sure I have the patience to prove my 8x8 hypothesis through brute force.

Wow! SudokuX without numbers! Incredilble! :)

Fun!

Neat. Brings to mind latin squares which I studied in some ancient time period.

Goto next topic

You must register and log in to be able to participate in this discussion.