Illuminations: Soda Cans

Soda Cans
Soda cans are placed on their side, in a box—four in the bottom row, three in the second row, four in the third row, and three in the top row. When the cans are shifted, some interesting things happen. What do you notice?

Instructions
 
Drag points A and B to move either of the middle cans on the bottom row. (The other cans in the arrangement will shift as a result.)

Click Show Line XZ to draw a line that passes through points X and Z.

Exploration
 
When you move the cans in the bottom row, what happens to the cans in the top row? For a major hint, click Show Line XZ.
  • Can you explain why this happens?
  • Will it work for arrangements with more cans in the bottom row? What if the width of the box is changed?
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