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The following image depicts the layers of a $5\times5\times5$ cube. Using 3-dimensional thinking, can you find the way out of the cube?

enter image description here
Empty version with no crossword numbers
Empty version with crossword only

1. Crossword (blue squares)

Across
1. Separately
4. Hurry
7. Physical or online locations
10. Caesar's planet
13. Venomous snake
14. Milan cathedral
15. Plantagenets and Lancasters
18. Avoid, escape
19. Slim, smooth

Down
1. Dumas character
2. Economic resource
3. Levels or makers of knots
10. Shy, fearful
11. Fictional Vietnam War veteran
12. Texas battle site
15. Clarinet, saxophone and others
16. A grave digger's tool or suit
17. Creep around

Away
1. Place where bridehood ends
2. A hectare is 2.5 –
3. Streetcars
4. Man in Paris
5. Music sometimes played with one note
6. Use a rubber
7. Dr Pepper and Mountain Dew, for example
8. Recurring theme, motif
9. Share in a company

2. Cryptic (yellow squares)

Across
7. Sticky substance from messy rupture (5)
8. No credit for one surrounded by debt (5)
11. Country to not get any introductions (5)
12. Small instrument making piece of furniture (5)

Down
5. Instruments for speakers of falsehoods called out (5)
6. Plant lit up, put out (5)
9. Troops destroyed, having lost second city (5)
10. Some pig looks for place to live (5)

Away
1. Piece of shiny long-lasting material (5)
2. Car infested with insects (5)
3. Airline is flying late after opening day (5)
4. Big boy misses opening of Golden Ox (5)

3. Statue View (red numbers)

Insert the eight given 3D-tromino pieces (seven L-shaped, one I-shaped) into the cube. Pieces may be rotated in any direction. (Remember, these are 3D pieces so use the Z-axis as well!) The resulting space must satisfy the rules1 of Statue View:
- Pieces cannot be adjacent to each other, but may touch at a corner.
- All unoccupied cells must be (orthogonally) connected.
- Any cells with red numbers must be unoccupied. These numbers give the total lengths of the runs of occupied cells starting immediately adjacent to the number, and extending outwards from it.

1 This puzzle type was invented by Deusovi and introduced in Statue View: Tetrominoes.

4. Maze

Starting from the central square and treating occupied cells as walls, find the shortest way out.

The final answer is what was required in order to escape the cube (two words).

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  • $\begingroup$ @wl Yeah, the Statue View should be possible to solve independently of the crossword parts. Where are you getting a contradiction? $\endgroup$ – jafe Jun 20 at 9:57
  • $\begingroup$ @OmegaKrypton I think you're confusing the yellow #6 with blue #6, no? (Maybe it would have been better to number them differently.) $\endgroup$ – jafe Jun 20 at 10:01
  • $\begingroup$ @wl D'oh, I see what you mean. Correcting this now... $\endgroup$ – jafe Jun 20 at 10:09
  • $\begingroup$ @wl Corrected now. (Found another error on the second layer as well.) Sorry about that. $\endgroup$ – jafe Jun 20 at 10:15
  • 1
    $\begingroup$ @jafe Solvable now. $\endgroup$ – w l Jun 20 at 10:22
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Solutions to the first three parts:


crossword clues, cryptics, and logic explanations

The maze:

maze solution To escape, you need the MASTER PLANS.

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  • $\begingroup$ Everything's correct. Nice job! $\endgroup$ – jafe Jun 20 at 12:51
  • $\begingroup$ Ninjaed you by one minute! But your answer had all the details immediately, whereas mine took a couple more minutes to write them down. @jafe, up to you whether you go by first answer or first answer with all the details... $\endgroup$ – Gareth McCaughan Jun 20 at 12:54
  • $\begingroup$ Small correction I missed on first glance: One of the dark green pieces needs a rotation to fix the 3 in the bottom layer. You guys had the solution at pretty much the same time, but Deusovi posted a complete solution first so I have accepted this one. Great job, both of you! $\endgroup$ – jafe Jun 20 at 16:22
5
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1. Crossword (blue squares)

enter image description here

Across

1. Separately

apart

4. Hurry

haste

7. Physical or online locations

sites

10. Caesar's planet

terra?

13. Venomous snake

mamba

14. Milan cathedral

duomo

15. Plantagenets and Lancasters

roses

18. Avoid, escape

evade

19. Slim, smooth

sleek?

Down

1. Dumas character

athos

2. Economic resource

asset

3. Levels or makers of knots

tiers

10. Shy, fearful

timid

11. Fictional Vietnam War veteran

rambo

12. Texas battle site
15. Clarinet, saxophone and others

reeds

16. A grave digger's tool or suit

spade [note: I have always thought this meant "a grave digger's suit" lol]

17. Creep around

sneak

Away

1. Place where bridehood ends

altar

2. A hectare is 2.5 –

acres

3. Streetcars

trams

4. Man in Paris
5. Music sometimes played with one note
6. Use a rubber

erase

7. Dr Pepper and Mountain Dew, for example

sodas

8. Recurring theme, motif

trope

9. Share in a company

stock

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  • $\begingroup$ Btw, the clue was "a grave digger's suit?" when first posted. I didn't like it when I reread the whole thing so I made an edit :) $\endgroup$ – jafe Jun 20 at 10:53
  • $\begingroup$ thanks... is anything wrong here? @jafe $\endgroup$ – Omega Krypton Jun 20 at 10:54
  • 1
    $\begingroup$ All correct so far! $\endgroup$ – jafe Jun 20 at 10:55
5
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You need the

MASTER PLANS.

Crosswords (Omega Krypton did a lot of these independently of me and probably earlier; I haven't looked at their answers) lead to these letters:

A P A R T
T N S B I
H A S T E
O D E B R
S I T E S

L L C T R
S Y R U P
O R A L R
D E B I T
O S R P T

T E R R A
I L A G L
M A M B A
I L B S M
D U O M O

A P E I M
T O N G A
M R B L S
S T O O L
A P P O C

R O S E S
E N P Y N
E V A D E
D A D N A
S L E E K

Statue View solution:

. . . . D
. . 4 D D
. H 1 . .
. . . . .
. . . . .

. . 2 . 3
. . A . .
  H 5 B 2
. . C . .
. . C . .

. . A . E
. . A 2 .
1 H 8 B B
. . C . .
. . 2 . .

. . . E E
. . 3 . 1
. 5 F . .
. . 3 . G
. . . . .

. . . . .
. . . . 2
. F F 3 G
. . . . G
. . . . 2

Brief explanation (i.e., transcription of my notes while solving the Statue View):

central 8 can only see 8 spaces, so fill them all
2 near it now has 2 blocks, so clear others
1 on middle layer sees what it needs, clear others
5 on second layer needs everything on the layer, so fill them in
2 on second layer now sees all the blocks it needs, so clear others
we have a few L-pieces; name them and clear their neighbours
1 on top layer has only one candidate neighbour, so use it
we've found the I-piece; name it and clear its neighbours
4 on top layer needs both neighbours there, so fill them in
other 2 on second layer has what it needs, clear rest
3 on second layer has neighbours only top/bot, can't have 3 bot, so give 1+2
found another L-piece, name and clear
1 on fourth layer has the neighbour it needs, clear others (actually already clear)
blocks in NE on layers 3 and 4 need to make L-piece, only one way so do it
3 on fourth layer has what it needs, so clear others
same for other 3 on fourth layer
5 on fourth layer has four neighbours, needs one more, only one way to do it
found another L, name and clear
now there is only one way to insert the final L, so do it

Maze solution by "flood-fill":

6 5 4 5 #
5 4 3 # #
6 # 2 3 4
5 4 3 4 5
6 5 4 5 6

7 6 5 6 7
6 5 # 7 6
7 # 1 # 5
6 5 # 5 6
7 6 # 6 7

8 7 # 7 #
7 6 # 8 7
8 # 0 # #
7 6 # 6 7
8 7 8 7 8

9 8 9 # #
8 9 A 9 8
9 A # A 9
8 9 A 9 #
9 8 9 8 9

A 9 A B A
9 A B A 9
A # # B #
9 A B A #
A 9 A 9 A

This

shows shortest distances from the starting cell; now we can work backwards from the end, finding the unique shortest path. It spells out MASTER PLANS.

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