## On the Subject of Clumsy Loopover

Get them up for me, Nickel. We've got some commutators to learn.

Use the arrow buttons to shift the rows and columns to arrange the 36 tiles into base-36 order.

Every row button also moves either the row above it or below it.

Every column button also moves either the column to the left or right of it.

### Notation

A move is notated as a pair consisting of an alphanumeric character followed by a direction and a number.

Letters denote moving pairs of columns: The letter A refers to columns 1 and 2, B refers to columns 2 and 3 and so on, with F referring to columns 6 and 1, wrapping around. Similarly, the number 1 refers to rows 1 and 2, the number 2 refers to rows 2 and 3, wrapping around.

As an example, A U2 refers to moving columns 1 and 2 up twice. 4 L1 refers to moving rows 4 and 5 left once. B U3 refers to moving columns 2 and 3 up three times.

Warning: the functionality of the buttons may differ from module to module. The move A U2 does not mean press the A button up twice!

### Algorithms

The following algorithms may prove useful in moving around tiles without affecting tiles already in their correct positions. Note that these algorithms all operate in the top-left 3 by 3 quadrant.

However, it is possible to translate which tiles the algorithm affects by translating the whole module. For example, if one wishes to apply an algorithm to the bottom-right quadrant, one may do the moves A 3, C 3, E 3, 1 3, 3 3, 5, 3 to move the bottom-right quadrant to the top-left, perform the algorithm, then undo the previous moves.

#### Basic algorithms

The following 8 algorithms form the basis of more advanced algorithms, which are labeled with bold capital letters.

 A A U1, 1 L1, A D1, 1 R1 B 1 L1, A U1, 1 R1, A D1 C 1 R1, B U1, 1 L1, B D1 D B U1, 1 R1, B D1, 1 L1 E B D1, 2 R1, B U1, 2 L1 F 2 R1, B D1, 2 L1, B U1 G 2 L1, A D1, 2 R1, A U1 H A D1, 2 L1, A U1, 2 R1

#### Advanced algorithms

Bold capital letters are shorthand for one of the eight basic algorithms. Many (many!) more algorithms are possible, however the ones below should suffice to solve the module. The below algorithms are known as commutators and conjugates (these terms originate from Rubik's cubes). Understanding commutators and conjugates will allow you to create many more algorithms.

 C B D A D, A, F D1, D, A, F U1 F D1, D, A, F U1, D, A H E G F F, C, 6 L1, F, C, 6 R1 6 L1, F, C, 6 R1, F, C