Covering 10 points, a surprisingly tricky puzzle.

2026-04-16 · Source: 3Blue1Brown · Field: Science & Research — Mathematics & Computational Sciences · Depth: Fundamental Awareness, quick

Summary

This month's puzzle challenges readers to determine if 10 arbitrary points on a two-dimensional plane can always be covered by a set of non-overlapping unit discs, each with a radius of one. The problem specifies that the discs must be disjoint, meaning they cannot overlap. For instance, if all 10 points are clustered closely together, a single unit disc might suffice to cover them. Conversely, if the points are widely dispersed, each point could potentially be covered by its own individual unit disc. The central question is whether this arrangement is universally achievable, regardless of the points' initial configuration on the plane.

Key takeaway

For mathematicians or puzzle enthusiasts seeking a geometric challenge, you should consider the implications of point distribution on disc placement. This puzzle requires rigorous logical thinking to determine if a universal solution exists for covering 10 points with non-overlapping unit discs. Your approach will need to account for both clustered and widely dispersed point configurations to prove or disprove the general claim.

Key insights

The puzzle explores the universal possibility of covering 10 arbitrary 2D points with disjoint unit discs.

Topics

• Geometric Puzzles
• Unit Discs
• Point Covering Problem
• Disjoint Sets
• Euclidean Geometry

Best for: General Interest

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Editorial summary, takeaway, and curation by AIssential. Original article published by 3Blue1Brown.