the king's balls

the king has a set of perfectly sphirical cristal balls, which he keeps in a chest which is a perfect rectangular prism on the inside. when one shakes the chest, nothing jiggels. if you take some of the balls out and rearange the balls, then still nothing jiggels. this can be done again, and again, and then once more. if each ball is 1 inch in diamiter, then what is the smallest # of balls and the smallest dimensions for the box possible?

Originally posted by fearlessleader
the king has a set of perfectly sphirical cristal balls, which he keeps in a chest which is a perfect rectangular prism on the inside. when one shakes the chest, nothing jiggels. if you take some of the balls out and rearange the balls, then still nothing jiggels. this can be done again, and again, and then once more. if each ball is 1 inch in diamiter, then what is the smallest # of balls and the smallest dimensions for the box possible?

Originally posted by Cheshire Cat
Smallest dimension of the box? or of the inside of the box?

~ Cheshire Cat 😀

1 x 1 x 2 working on the premise that one can include the balls taken out when rearranging them in the box.

Originally posted by fearlessleader
the king has a set of perfectly sphirical cristal balls, which he keeps in a chest which is a perfect rectangular prism on the inside. when one shakes the chest, nothing jiggels. if you take some of the balls out and rearange the balls, then still nothing jiggels. this can be done again, and again, and then once more. if each ball is 1 inch in diamiter, then what is the smallest # of balls and the smallest dimensions for the box possible?

Originally posted by iamatiger
Are the balls distinct, ie can a triangle of three touching balls be arranged in 2 (mirror image) ways?

Originally posted by Acolyte
I read it that each time the balls are rearranged, balls are also removed, leading to a configuration which is necessarily distinct.

Is the inside of the box completely rigid?