Question 12
Alex the beaver is assigned to put balls into a wooden box with nine compartments as illustrated below.
There are nine balls, but Alex may choose how many to put in the box. The placement must satisfy all the following conditions:
- Each ball is placed neatly into one of the nine compartments; all nine are wide 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 placements satisfy the conditions?
There are nine balls, but Alex may choose how many to put in the box. The placement must satisfy all the following conditions:
- Each ball is placed neatly into one of the nine compartments; all nine are wide 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 placements satisfy the conditions?