The image below shows a pool rack with 15 billiard balls which fit perfectly within the rack
(i.e. there is no extra space for any of the balls to move).

Note that the rack above is slightly smaller than an actual/standard pool rack in which there is a
small amount of space between the rack and the balls.

What is the maximum number of balls that can be removed from the rack such that the remaining balls
are still immobilized (i.e. unable to move)?

**ANSWER**:

*6 is the maximum number of balls that can be removed.*
**EXPLANATION**: See the image below:

If you don't see why the 4-ball or 8-ball (for example) are immobilized, the image below shows
you the size of these balls relative to the space they would need to pass through:

And if your answer was 10, thinking along the lines of the image below:

Because it was possible to place the 5-ball between the 12-ball and 10-ball (for example), it must also
be possible to remove it, therefore the balls are not immobilized in the image above and 10 is not a
valid answer. You can try it yourself by lining up three cups or plastic bottles. You will be able to
slide the middle bottle out without moving either of the other two bottles.

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?