Solution
Moser's Circle
Show the problem again
Six points are placed on a circle and every pair is joined by a chord, with no three chords meeting at a single interior point. Into how many regions is the disk divided?
Worked solution
The answer is 31. The counts for 1–5 points are 1, 2, 4, 8, 16, tempting the guess 32, but the true formula is 1 + C(n,2) + C(n,4) (via Euler's formula: each chord adds a region, and each interior intersection, one per 4-subset of points, adds another). For n = 6: 1 + 15 + 15 = 31. A famous warning against extrapolating patterns.
Source: Circle division by chords, a counting trap studied by Leo Moser. Statement written for AxiomIQ.