Solutions of ponderables of David Joyner’ book Adventures in group theory

This page lists the doable ponderables, even the easiest ones, but I don’t recall explicitely their content. Sometimes, I enlarge the question.

Sometimes, I use Werner Randelshofer’s Rubik’s cube Java applet with Singmaster’s notation.

Elementary, My dear Watson

You have a logical mind if…

• Ponderable 1.1.1
• Ponderable 1.1.2
• Ponderable 1.1.3
• Ponderable 1.1.4
• Ponderable 1.1.5
• Ponderable 1.1.6
• Ponderable 1.1.7

Elements, my dear Watson

• Ponderable 1.2.1
• Ponderable 1.2.2

‘And you do addition?’

Functions

• Ponderable 2.1.1
• Ponderable 2.1.2
• Ponderable 2.1.3
• Ponderable 2.1.4
• Ponderable 2.1.5
• Ponderable 2.1.6
• Ponderable 2.1.7

Functions on vectors

• Ponderable 2.2.1
• Ponderable 2.2.2

Relations

• Ponderable 2.3.1
• Ponderable 2.3.2
• Ponderable 2.3.3
• Ponderable 2.3.4

Counting and mathematical induction

• Ponderable 2.4.1

Bell ringing and other permutations

Definitions

• Ponderable 3.1.1
• Ponderable 3.1.2
• Ponderable 3.1.3
• Ponderable 3.1.4

Inverses

• Ponderable 3.2.1
• Ponderable 3.2.2

Cycle notation

• Ponderable 3.3.1
• Ponderable 3.3.2
• Ponderable 3.3.3

An algorithm to list all the permutations

Bonus: a Python script that lists all the permutations with a generator and that computes the product of permutations (from left to right).

Permutations and bell ringing

No ponderable.

A procession of permutation puzzles

15 Puzzle

• Ponderable 4.1.1
• Ponderable 4.1.2

The Hockeypuck puzzle

• Ponderable 4.2.1

Rainbow Masterball

• Ponderable 4.3.1
• Ponderable 4.3.2
• Ponderable 4.3.3

Pyraminx

• Ponderable 4.4.1

Rubik’s Cubes

• Ponderable 4.5.1
• Ponderable 4.5.2
• Ponderable 4.5.3
• Ponderable 4.5.4

Skewb

• Ponderable 4.6.1

Megaminx

• Ponderable 4.7.1
• Ponderable 4.7.2

Other permutation puzzles

No ponderable.

What’s commutative and purple?

The unit quaternions

No ponderable.

Finite cyclic groups

No ponderable.

The dihedral group

No ponderable.

The symmetric group

• Ponderable 5.4.1

General definitions

• Ponderable 5.5.1
• Ponderable 5.5.2
• Ponderable 5.5.3
• Ponderable 5.5.4

Subgroups

• Ponderable 5.6.1
• Ponderable 5.6.2

Puzzling examples

• Ponderable 5.7.1
• Ponderable 5.7.2

Commutators

• Ponderable 5.8.1
• Ponderable 5.8.2
• Ponderable 5.8.3
• Ponderable 5.8.4
• Ponderable 5.8.5

Conjugation

• Ponderable 5.9.1
• Ponderable 5.9.2
• Ponderable 5.9.3
• Ponderable 5.9.4
• Ponderable 5.9.5
• Ponderable 5.9.6
• Ponderable 5.9.7
• Ponderable 5.9.8
• Ponderable 5.9.9
• Ponderable 5.9.10
• Ponderable 5.9.11

Orbits and actions

• Ponderable 5.10.1
• Ponderable 5.10.2
• Ponderable 5.10.3
• Ponderable 5.10.4
• Ponderable 5.10.5
• Ponderable 5.10.6
• Ponderable 5.10.7
• Ponderable 5.10.8
• Ponderable 5.10.9
• Ponderable 5.10.10

Maison