Question

Shown below is an arrangement of closely stacked spheres. Assume each one to be in contact with its immediate neighbour. What is the total number of points where the spheres touch each other?

Hint:

In problems involving closely packed arrangements, visualize the pattern of connections, and use geometric relationships to count the points of contact.

Answer 1

Step 1: In a closely stacked arrangement, each sphere touches several others. Start by counting how many points of contact each row has.
Step 2: Given the triangular arrangement, each sphere touches 6 others in the next layer. By examining the structure, we calculate the total number of touching points across all layers.
Step 3: The total number of points where the spheres touch each other in this configuration is 96.