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?

Smallest dimension of the box? or of the inside of 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?

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.