Question 11
Alex the beaver is asked to place balls in a wooden box with nine compartments, as illustrated below.
There are nine balls in total, but Alex may choose how many to put in the box. The arrangement must also satisfy all these conditions:
- Every ball in the box is placed neatly in one of the nine compartments (all nine compartments are large enough to hold a ball).
- Each compartment contains at most one ball.
- The total number of balls in every row and every column is odd.
How many different arrangements satisfy these conditions?
There are nine balls in total, but Alex may choose how many to put in the box. The arrangement must also satisfy all these conditions:
- Every ball in the box is placed neatly in one of the nine compartments (all nine compartments are large enough to hold a ball).
- Each compartment contains at most one ball.
- The total number of balls in every row and every column is odd.
How many different arrangements satisfy these conditions?