The Series

All 20 Puzzles

Ordered for learning, not difficulty alone. Numbers are display positions; the five arcs build on one another.

Arc 1 · Things Are Not What They Seem
1

The Gatekeeper

Unknot recognition
Beginner Disentanglement
▶ Open in explorer #1
2

Shepherd's Yoke

Buttonhole homotopy
Beginner Disentanglement
▶ Open in explorer #2
3

The Prisoner's Ring

Linking number cancellation
Beginner-Intermediate Disentanglement
▶ Open in explorer #3
4

Mobius Snare

Non-orientability (Mobius boundary)
Intermediate Disentanglement
▶ Open in explorer #4
5

The Mirror Gate

Chirality (handedness)
Intermediate Identification
▶ Open in explorer #5
Arc 2 · Structure Matters
6

Trinity Lock

Borromean rings (no pairwise linking)
Intermediate Assembly
▶ Open in explorer #6
7

Devil's Pitchfork

Fundamental group of configuration space
Intermediate-Advanced Transfer (manipulation)
▶ Open in explorer #7
8

The Ferryman's Knot

Open knot vs. closed knot; Reidemeister moves on constrained arcs
Advanced Disentanglement
▶ Open in explorer #8
9

The Crossing Number

Unknotting number (crossing changes)
Beginner-Intermediate Transformation
▶ Open in explorer #9
Arc 3 · Deep Mathematics Is Physical
10

Ouroboros Chain

Gray code / binary recursion (Chinese Rings reimagined)
Advanced Sequential disentanglement
▶ Open in explorer #10
11

Genus Trap

Genus-2 surface fundamental group
Expert Disentanglement
▶ Open in explorer #11
12

The Hopf Paradox

Hopf fibration / coupled rotation in S^3
Expert Extraction
▶ Open in explorer #12
Arc 4 · Classification and Construction
13

The Braid Cage

Braid groups (Yang-Baxter relation)
Intermediate-Advanced Transfer
▶ Open in explorer #13
14

The Torus Winder

Torus knots — (p,q) winding numbers
Advanced Assembly
▶ Open in explorer #14
15

The Tricolor Lock

Fox tricolorability (knot invariant)
Intermediate Assembly
▶ Open in explorer #15
16

The Seifert Sail

Seifert surfaces (surfaces bounded by knots)
Advanced Assembly (surface construction)
▶ Open in explorer #16
17

The Satellite Trap

Satellite knots (JSJ decomposition)
Expert Extraction
▶ Open in explorer #17
Arc 5 · The Limits and Language of Invariants
18

The Whitehead Waltz

Whitehead link — linking number zero without splittability
Advanced Identification / Disentanglement
▶ Open in explorer #18
19

The Tangle Dance

Conway rational tangles — the fraction is a complete invariant
Intermediate-Advanced Sequential transformation
▶ Open in explorer #19
20

The Granny's Downfall

Connected sums — composite knots and chirality under composition
Advanced Identification / Assembly
▶ Open in explorer #20