Queens as logic
One queen in every row, every column and every region, and no two queens touching. Four sentences again.
How it works
A Queens board is an n×n grid cut into n colored regions. You place n queens. The rules are short.
Every row has exactly one queen. Every column has exactly one queen. Every region has exactly one queen. No two queens touch, not even at a corner.
The first three are the same “exactly one” sentences as sudoku, with queens in place of digits. The fourth is a “for every pair” sentence: for every two queens, they are not neighbors. That one does most of the work.
Where the n queens come from
The rules never say “place five queens”. They don’t need to. There are five rows, and each has exactly one queen, so there are five queens. Counting follows from the rules.
The same count works for columns and regions. That is why a Queens board always has as many regions as rows.
The touching rule is the strong one
A queen away from the edge rules out its row, its column, its region and eight neighbors. The neighbors are the part people forget, and they are where most deductions come from.
Worth memorizing
One queen per row, per column, per region.
Three “exactly one” sentences.
No two queens touch, even diagonally.
A queen rules out all eight neighbors.
n rows means n queens and n regions.
Practice
0 of 5 rightWhy can’t a queen go on the ringed cell?
Why can’t a queen go on the ringed cell?
Why can’t a queen go on the ringed cell?
How many queens does this board need?
How many cells does this one queen rule out?