Solutions Page

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Solutions Page		Last updated:Jan 23, 2009

Fiendish15
Dial Trouble
Reverse Pegs
Arrow
4x4x5 Cuboid
Rubik's Mate (3x1x1 edge bandage)

Fiendish15

This puzzle is always soluble.

Notation examples:
B1 = Box or cell 1 regardless of which slider is in it. (Top row is B1,B2,B3,B4 etc)
S1 = Slider 1 regardless of which box it is in.
1D = move S1 down 1.
1D2 = move S1 down 2.
B1D = move slider in Box 1 down 1.

Notes:
These moves will involve moving other sliders out of the way first. However do not move a slider that is already solved (ie smaller than the step number) unless explicitly indicated below.

Level 1

Move S1 to B1. If upside down move 1D, 1R, 1U, 1L
Move S2 to B2. If upside down move 2D, 2R2, 2U, 2L2
Move S3 to B3. If upside down move 3D, 3R, 3U, 3L
If S4 positioned correctly go to step 5.
If S4 in position but upside down: 2D, 3L, 4L, 4D, 4R, 4U, 3R, 2U, go to step 5
If B4 is empty and S4 is in B8 move 4U, restart step 4
Move S4 to B8.
If S4 is at angle 8 o'clock move 4L, 4D2, 4R, 4U2
Get S4 into B4 by 2D, 3L, 4U, 3R, 2U
Move S5 to B5. If upside down move 5D2, 5R, 5U2, 5L
Move S6 to B6. If upside down 6D, 6R, 6U, 6L
Move S7 to B7. If upside down 7D2, 7R, 7U2, 7L
If S8 in position correctly go to step 9.
If S8 in position but upside down: 6D, 7L, 8L, 8D, 8R, 8U, 7R, 7U, go to step 9
If B8 is empty and S8 is in B12 move 8U, restart step 8
Move 8 to B12.
If S8 is at angle 8 o'clock move 8L, 8D, 8R, 8U
Get S8 into B8 by 6D, 7L, 8U, 7R, 6U
Move S9 to B9. If upside down move 9D, 9R, 9U, 9L
Move the all the bottom row to the left, if possible.
a) If S10 is in B13: 10R, 9D, 10U, 10R, 9U, 10L go to step 10.c
b) Move 10 to B10.
c) If upside down 10D, 10R2, 10U, 10L2
Move the all the bottom row to the left if possible.
a) If S11 is in B13: 11R, 9D, 10L, 11U, 11R, 10R, 9U go to 11.d
b) If S11 is in B14: 11R, 9D, 10L, 11U, 10R, 9U go to 11.d
c) Move S11 to B11.
d) If upside down 11D, 11R2, 11U, 11L2
Move the all the bottom row to the left if possible.
a) If S12 is in B13: 12R, 9D, 10L, 11L, 12R, 9R, 10D, 11L, 12U, 12R, 11R, 10U, 9L, 11R, 10R, 9U. If ok goto step 13, if upside down goto 12.d
b) if S12 is in B14: 12R, 9D, 10L, 11L, 12U, 12R, 11R, 10R, 9U. If ok goto step 13, if upside down goto 12.d
c) if S12 is in B15: 12R, 9D, 10L, 11L, 12U, 11R, 10R, 9U.If ok goto step 13, if upside down goto 12.d
d) if S12 is upside down: 9D, 10L, 11L, 12L, 12D, 12R, 12U, 11R, 10R, 9U
Move the all the bottom row to the left if possible.

a) If solved start new game.
b) If S13 not in correct position: 9D, 10L, 11L, 12L, 9R, 10D, 11L, 12L. Now move S13 to B15. Then move 12R, 11R, 10U, 9L, 12R, 11R, 10R, 9U, 13L, 14L, 15L. If solved start new game.
c) Some sliders are not correct angle:
ci) All upside down: 9D, 10L, 11L, 12L, 9R, 10D, 11L, 12L. 15L - 15D, 15R, 15U - 12R, 11R, 10U, 9L, 12R, 11R, 10R, 9U, 13L, 14L, 15L. Solved!
cii) I will not detail the remaining 6 permutations but will describe the principle. If you have got B16 empty and you repeat B15R, B11D, B12R, B16U 3 times (call this circuit move 1) then the 3 sliders in B11, B12, B15 will have inverted (ci is an example of this). If you started with 1 of B11, B12, B15 upside down you will end up with 2 upside down and this is the crux.

You are aiming to increase the number of upside down sliders from 2 to 3 or 1 to 2 then 2 to 3 until you have 3 upside down sliders at which point you can invert them all. Increase the number of upside down sliders by bringing one upside down slider and 2 right way sliders (choose from S9-S15) into B11, B12, B15, B16. Make the move indicated above and return all sliders to their correct positions ensuring they all return via the same path they came along.

Level 2
This proceeds like level 1 until step 13, except that when a slider is in the wrong orientation it might have to be taken twice along the path indicated in level 1. This is because there are two wrong orientations for a slider.

Step 13: Move all the bottom row to the left.

a) If solved start new game

b) If S13 not in correct position: 9D, 10L, 11L, 12L, 9R, 10D, 11L, 12L. Now move S13 to B15. Then move 12R, 11R, 10U, 9L, 12R, 11R, 10R, 9U, 13L, 14L, 15L. If solved start new game.

Otherwise one of the following will be the case:
One slider not aligned – convert to cii using circuit move 1 or its reverse.
Two sliders not aligned pointing the same way – align 11, 12 and 15 the same way as the two sliders in question using the circuit move 1 or its reverse. Now you have five sliders not aligned pointing the same way - see below.
Two sliders not aligned pointing different ways – treat as two separate cases of ci.
Three sliders not aligned all pointing the same way – use circuit move 1 or its reverse.
Three sliders not aligned two pointing the same way – convert to cii using circuit move 1, then solve as cii
Three sliders not aligned all pointing different ways - convert to cii using circuit movee 1, then solve as ciii

Five not aligned pointing the same way – get the five sliders in question into B10,B11,B12,B14 and B15 (B16 empty). Rotate this ring clockwise or anticlockwise as necessary. Then return the sliders to their correct positions along the same paths they were brought together on.

Level 3

Note that B3 and B8 contain identical sliders. If you cannot complete the puzzle as illustrated you will have to swap those two pieces.
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Dial Trouble

Terminology

SR: small rings clockwise
SL: small rings anticlockwise
LR: large ring clockwise
LL: large ring anticlockwise
A: SL, LL, SL, LR
B: SR, LL, SR, LR
P0: position of 0 when solved
P1-P9 likewise

Note that the sequence ABBA swaps 7 with 2 and 0 with 1.

First get 8 and 9 into position. This should be easy.

Ensure 6 is in the main ring. Use ABBA if necessary.

Next get 5 next to the 6.

If 5 is in P0 place it in the main ring thus

Ensure 6 is not in P1, P2 or P7. ABBA

If 5 needs to be moved 1 space clockwise

Put 6 in P3. SR ABBA SL

If 5 needs to be moved 2 spaces clockwise

Put 6 in P3. ABBA

If 5 needs to be moved 3 spaces clockwise

Put 6 in P4. ABBA. Put 6 in P3. SR ABBA SL

If 5 needs to be moved 4 spaces clockwise

Put 6 in P5. ABBA. Put 6 in P3. ABBA

If 5 needs to be moved 5 spaces clockwise

Put 6 in P6. ABBA. Put 6 in P4. ABBA. Put 6 in P3. SR ABBA SL

Then get 4 next to the 5.

Adapting the moves from the previous step.
If 4 is in P0 place it in the main ring thus

Ensure neither 5 or 6 is in P1, P2 or P7. ABBA

If 4 needs to be moved 1 space clockwise

Put 5 in P3. SR ABBA SL

If 4 needs to be moved 2 spaces clockwise

Put 5 in P3. ABBA

If 4 needs to be moved 3 spaces clockwise

Put 5 in P4. ABBA. Put 5 in P3. SR ABBA SL

If 4 needs to be moved 4 spaces clockwise

Put 5 in P5. ABBA. Put 5 in P3. ABBA

Then get 3 next to the 4.

Adapting the moves from the previous step.
If 3 is in P0 place it in the main ring thus

Ensure none of 4, 5 or 6 is in P1, P2 or P7. ABBA

If 3 needs to be moved 1 space clockwise

Put 4 in P3. SR ABBA SL

If 3 needs to be moved 2 spaces clockwise

Put 4 in P3. ABBA

If 3 needs to be moved 3 spaces clockwise

Put 4 in P4. ABBA. Put 4 in P3. SR ABBA SL

Then get 2 next to the 3.

Adapting the moves from the previous step.
If 2 is in P0 place it in the main ring thus

Ensure none of 3, 4, 5 or 6 is in P1, P2 or P7. ABBA

If 2 needs to be moved 1 space clockwise

Put 3 in P3. SR ABBA SL

If 2 needs to be moved 2 spaces clockwise

Put 3 in P3. ABBA

Finally

At this point you have the 0,1 and 7 in the upper small ring. If these are in the correct position the puzzle is solved.
If not the following sequence will rotate the upper ring anticlockwise (apply once or twice):
LL ABBA LR ABBA LL SR ABBA SL ABBA LR

Reverse Pegs

Notation

P1-P12 = Possible peg positions starting at the left
T = rotate
nL1 = move peg in Pn left by 1
mL4 = move peg in Pm right by 4
etc

Level 1

This should be fairly simple – I'll give a solution for the fixed start position shown.

To obtain the fixed start position press f on the java version of this puzzle.

screen shot

For the first 4 pegs work from left to right.

1. move yellow from P12 to position P1: 12L4 T 2R3 T 1R4 T 6L2 T 3R2 T 5L4 screen shot

2. move cyan from P10 to position P2: 10L2 T 8R1 T 4R1 T 5L3 screen shot

3. move white from P11 to P3: 11L3 T 4R3 T 5L2 screen shot

4. move red from P12 to P4: 12L4 T 8R1 T 4R1 T 5L1 screen shot

Now work right to left, leaving pegs 1 to 4 untouched.

5. move green from P7 to P12: 6R1 T 10L2 T 8R4 screen shot

6. move magenta from P6 to P11: 6R2 T 9L1 T 8R3 screen shot

7. move blue from P5 to P10: screen shot T 8R2

8. move orange from P7 to P9 : 7R2

Level 2

This is similar to Level 1. However once you have completed the first four pegs every second rotation will swap 2 and 4. Thus you may end up in one of two positions (unless you have solved it).

One (2 and 4 reversed)

screen shot

10L2 T 5R4. This will put you in position two – proceed as below.

Two (9 and 10 reversed)

screen shot

12L1 T 5R4 T 10L2 T 12L4 T 5R4

The principle is to get pegs 9-12 in the reverse order using an odd number of rotations, then move them to the large ring to rotate them into the correct order. The whole sequence therefore uses an even number of rotations.

Level 3

Start from the left getting pegs 1-4 in order. Then working from the right attempt to get pegs 12-10 in order. Remember every second rotation leaves 2 and 4 swapped.
Here are the main positions you might end up in

screen shot

Here 2 and 4 are reversed:
T 9R1 (now you're in the position shown below)

screen shot

Here 10 and 11 are reversed:
10L2 T 12L1 T 8R2 T 12L1 T 9R1 (*)
This move leaves all other pegs in the same position!

At this point consider the remaining three pegs: 5, 8 and 9.
If they are in the right order, just slide them into position.
Otherwise use the moves below as required until the puzzle is solved.

This move takes whatever is in position 5 and puts it in position 8:
12L2 T 5R1 T 5R2 T 12L1 T 11L1 T 8R1 T 9R1
So if you have:
screen shot

you end up with:
screen shot

(In this particular example the puzzle is actually solved – just slide the three pegs into position.)

However if you cannot solve the puzzle by the one or two applications of the move above you will have to use the swap move below first.

This move swaps the pegs in 5 and 6:
(The principle here is to move 5 and 6 into the small ring, apply the swap above (*) then return the two pegs to the large ring)
11L2 T 7R2 T * T 10L1 T 7R2 T 9L1 T
So if you have:
screen shot

you will end up with:
screen shot

This particular example is solved.

Arrow
Notation
Simple Moves

L= move shaft left,
R= move shaft right,
C= spin the arrow head clockwise,
A= spin the arrow head anticlockwise.

2L= shorthand for L L etc
2C= shorthand for C C etc
*L= move shaft fully left
*R= move shaft fully right

Position Numbers

8
1 2 3 4 5 6 7 . . . .
9

Key Position Names

7 = Point
8 = Top Tip
9 = Bottom Tip
7,8,9 = Tips
5,6,7,8,9 = Spinner
1-7 = Shaft

Colours at each position

1 = Red
2 = Orange
3 = Yellow
4 = Green
5 = Blue
6 = Magenta
7 = White
8 = Light Magenta
9 = Dark Magenta

Useful sequences

Top Swap (TS)

4R 2C 2L 2C 2L C 4R 3C 2L C 2L
This sequence will swap 8 and 7 (level 1)
If applied twice the effect is to invert 7 and 8 (level 2)

Bottom Swap (BS)

4R 2C 2L 2C 2L 3C 4R C 2L 3C 2L
This sequence will swap 7 and 9 (level 1)
If applied twice the effect is to invert 7 and 9 (level 2)

Point Swap (PS)

4R C L C 2L 3C 3R C L 2C 2L C R 3C 2L C R 3C L 2C
This sequence will swap 6 with 7 and 8 with 9 (level 1)

Point Rotate (PR)

2R C 2L 3C 2R 2C 2L 2C
This rotates 7,8,9 anticlockwise (level 1)

Quarter turn (QT)

R C L 2C R C L 2C
This orients 5 and 7 from up/down to left/right (level 3)

Half turn (HT)

3R C 3L 2C 3R C 3L 2C
This orients 3 from left to right (level 3)

Level 1
To get started

Working from left to right get Red, Orange, Yellow and Green into position.
Move the shaft fully left.

Blue

If Blue is not at the centre of the Spinner, spin it into position.
Otherwise use Point Swap and spin Blue into position.

Magenta

If this is in position move on to solve the Tips.
If Magenta is at the Point use Point Swap
If Magenta is at the Top or Bottom Tips, use Top Swap or Bottom Swap to get it to the Point, then use Point Swap

Solve the Tips (Light Magenta, Dark Magenta, White)

Use Top Swap and Bottom Swap to sort them out

Level 2

To get started

Working from left to right get Red and Orange correctly positioned and oriented.

Get Yellow and Green into position, but not necessarily correctly oriented (the orientation will change in the steps below).

Blue

If Blue can be spun into position, do so.
If Blue is is the centre of the spinner use: R C L TS R C L

Magenta

From now on we apply useful sequences in pairs, sometimes with simple moves before, between and after. This preserves the orientation of completed colours
If Magenta is in position move on to Final Stages.
If Magenta is at the Point:

C PS 3C PS

Spin Blue into position
Move on to Final Stages

If Magenta is at Top or Bottom Tips

Use Point Swap

Rotate Magenta to Point
Use Point Swap again
Spin Blue into position
Move on to Final Stages

Final stages

If Yellow is pointing the wrong way: 2R C 2L TS TS 2R 3C 2L
If Green is pointing the wrong way: R C L TS TS R 3C L
If Magenta is pointing the wrong way: PS PS
Get the 3 tips (Light Magenta, Dark Magenta, White) into position with an even number of Top Swaps and Bottom Swaps. This might involve swapping the blue.
If Blue is pointing the wrong way: C TS TS 3C
If Top Tip and Point are pointing the wrong way: TS TS
If Bottom Tip and Point are pointing the wrong way: BS BS
If Top and Bottom Tips are pointing the wrong way: TS TS BS BS

Level 3

To get started

Get Red in position and correctly oriented.

Working from left to right get Orange, Yellow, Green in position and oriented either left or right (not up or down)

Blue

If Blue is in centre of spinner:

Use PS to swap it with another colour.
Rotate the spinner and use PS again (to keep O,Y,G oriented left or right)
Spin blue into position

Magenta (Centre)

If in centre move to next stage
If not in centre use PS twice (once on Blue, Dark Magenta, Light Magenta or White, secondly on Magenta)

White, Dark Magenta, Light Magenta

If all in position move to next stage
If not in position use TS twice intermixed with C.

Reorient balls that are pointing up/down to be left/right

If Magenta Centre is up/down use PS PS
If 5 and 7 are up/down: QT
If 8 and 9 are up/down: C QT A
If two adjacent balls of 5,7,8,9 are up/down:

spin the balls into positions 5,8
TS QT TS
spin the balls back to their original positions

Finally reverse any balls that are pointing left

Clever use of HT can now reverse any ball in pointing left.
Here is an example to reverse ball 8 (gets ball 8 to 3, reverses it and returns it to its proper position):

2R A 2L
HT
2R C 2L