Let's play mini-Sudoku! size(3cm); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,black+2bp); draw((0,2)--(4,2),black+2bp); draw((2,0)--(2,4),black+2bp); draw((0,1)--(4,1)); draw((0,3)--(4,3)); draw((1,0)--(1,4)); draw((3,0)--(3,4)); We wish to place an "X" in four boxes, such that there is exactly one "X" in each row, column, and 2x2 outlined box. For example: size(3cm); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,black+2bp); draw((0,2)--(4,2),black+2bp); draw((2,0)--(2,4),black+2bp); draw((0,1)--(4,1)); draw((0,3)--(4,3)); draw((1,0)--(1,4)); draw((3,0)--(3,4)); label("X",(0.5,1.5)); label("X",(1.5,3.5)); label("X",(2.5,2.5)); label("X",(3.5,0.5)); In how many ways can we do this?$$Let's play mini-Sudoku!
size(3cm);
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,black+2bp);
draw((0,2)--(4,2),black+2bp);
draw((2,0)--(2,4),black+2bp);
draw((0,1)--(4,1));
draw((0,3)--(4,3));
draw((1,0)--(1,4));
draw((3,0)--(3,4));
We wish to place an "X" in four boxes, such that there is exactly one "X" in each row, column, and 2x2 outlined box. For example:
size(3cm);
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,black+2bp);
draw((0,2)--(4,2),black+2bp);
draw((2,0)--(2,4),black+2bp);
draw((0,1)--(4,1));
draw((0,3)--(4,3));
draw((1,0)--(1,4));
draw((3,0)--(3,4));
label("X",(0.5,1.5));
label("X",(1.5,3.5));
label("X",(2.5,2.5));
label("X",(3.5,0.5));
In how many ways can we do this?$$
