Each puzzle is a physical object — rod, ring, cord, frame — that looks trapped and isn't, or looks free and won't come loose. The trick is always a theorem. Read it, rotate it in 3D, watch it solve, then build it.
Five Arcs
A learning sequence
Arc 1
Things Are Not What They Seem
Puzzles 1–5Unknots, model inversion, linking number, non-orientable surfaces, and chirality — first lessons in topological intuition.
Arc 2Structure Matters
Puzzles 6–9Brunnian links, Borromean rings, multi-step disentanglement, and the unknotting number.
Arc 3Deep Mathematics Is Physical
Puzzles 10–12The Hopf link, genus and handles, and the Hopf fibration made tactile.
Arc 4Classification and Construction
Puzzles 13–17Braid groups, torus knots, tricolorability, Seifert surfaces, and satellite knots.
Arc 5The Limits and Language of Invariants
Puzzles 18–20Where linking number fails, where the Conway fraction succeeds, and what connected sums hide from your invariants.
The Series
20 puzzles
1
The Gatekeeper
Unknot recognition ▶ Open in explorer #1
2
Shepherd's Yoke
Buttonhole homotopy ▶ Open in explorer #2
3
The Prisoner's Ring
Linking number cancellation ▶ Open in explorer #3
4
Mobius Snare
Non-orientability (Mobius boundary) ▶ Open in explorer #4
5
The Mirror Gate
Chirality (handedness) ▶ Open in explorer #5
6
Trinity Lock
Borromean rings (no pairwise linking) ▶ Open in explorer #6
7
Devil's Pitchfork
Fundamental group of configuration space ▶ Open in explorer #7
8
The Ferryman's Knot
Open knot vs. closed knot; Reidemeister moves on constrained arcs ▶ Open in explorer #8
9
The Crossing Number
Unknotting number (crossing changes) ▶ Open in explorer #9
13
The Braid Cage
Braid groups (Yang-Baxter relation) ▶ Open in explorer #13
14
The Torus Winder
Torus knots — (p,q) winding numbers ▶ Open in explorer #14
15
The Tricolor Lock
Fox tricolorability (knot invariant) ▶ Open in explorer #15
16
The Seifert Sail
Seifert surfaces (surfaces bounded by knots) ▶ Open in explorer #16
17
The Satellite Trap
Satellite knots (JSJ decomposition) ▶ Open in explorer #17
18
The Whitehead Waltz
Whitehead link — linking number zero without splittability ▶ Open in explorer #18
19
The Tangle Dance
Conway rational tangles — the fraction is a complete invariant ▶ Open in explorer #19
20