Question

What is the maximum number of circular discs of equal size, which can be placed around a similar disc, such that the central disc is touched by all others but there is no overlap between any of the discs?

• A. 6
• B. 8
• C. 12
• D. 10

Hint:

This concept is related to the “kissing number” problem in geometry, where in 2D the kissing number is 6.

Answer 1

The Correct Option is A

Step 1: Understanding the geometric arrangement.
When circular discs of equal radius are arranged around one central disc so that each touches the center disc but not each other, the problem becomes one of circle packing in a plane.
Step 2: Explanation.
In two dimensions, six circles can be arranged around one central circle such that all outer circles touch the central circle without overlapping. This forms a perfect hexagonal pattern.
Step 3: Conclusion.
Hence, the maximum number of discs that can be placed around one disc is six.