In Act II, some puzzles are entangled with one in the opposite dimension. The two puzzles each have their own theme, core mechanic, answer, and solution, but each requires some information or action from the other in order to solve. This puzzle is entangled with Tumbled Tower.
As clued by the title, the grid at the top is an Akari logic puzzle, but with an irregular grid shape where cells of various sizes can be adjancent to each other. This gives the puzzle some unique geometry but otherwise the rules are the same as a standard Akari. Here is an explanation of a possible logical solve path for the Akari:
=HYPERLINK("https://youtu.be/gX-tbZR1X9w", "Link to video")
There are some blanks at the bottom of the puzzle that indicate phrases of some sort should be filled in. However there seem to be no ways to extract letters from just the Akari solution! At this point, we need the heptominoes from Tumbled Tower. Each heptomino from that puzzle has letters on each square as seen in the solution to that puzzle.
The next step is to place each heptomino from Tumbled Tower into the Akari grid. At first this seems underconstrained, but there are a couple additional restrictions that help us make logical progress. If we count the number of heptominoes and number of lightbulbs, we notice there are 19 of each. Furthermore, there are 133 squares in the Akari grid and 133 = 7*19 squares in total among the heptominoes. This suggests that the heptominoes should be placed without overlap into the Akari grid such that each heptomino contains exactly one lightbulb. We are also given an initial letter M in the top left corner as a starting point.
With this understanding of the puzzle, there is a logical path to uniquely placing the heptominoes into the grid. The key insight for placing each heptomino is to look at specific squares in the grid and notice that the given heptomino is the only one that can cover that square. Here is the completed grid (colors only for distinguishing heptominoes):
M
A
C
B
R
D
2
O
0
N
1
I
J
O
E
H
O
U
S
L
E
0
Y
U
3
S
E
0
E
B
D
I
P
P
R
I
B
O
O
M
C
E
0
0
E
T
0
0
E
E
V
L
1
0
R
F
N
0
0
R
R
0
T
K
D
O
O
P
I
I
I
R
P
S
T
S
S
2
2
E
E
N
R
0
L
I
G
2
A
H
1
U
T
F
0
G
1
R
S
R
D
P
L
A
N
H
L
G
O
L
F
O
R
0
0
E
E
0
1
C
B
C
E
0
0
T
2
G
0
0
A
E
A
I
D
I
P
S
K
E
A
W
S
P
P
0
B
N
M
A
0
J
H
S
I
L
G
N
E
1
Q
1
C
0
T
E
J
N
I
One possible order in which the heptominoes can be logically placed is depicted below:
M
A
D
E
B
T
E
V
N
R
U
D
C
I
O
J
O
E
E
Y
U
C
B
R
U
S
L
I
N
H
O
S
I
B
O
E
O
M
C
E
E
R
B
D
I
P
P
R
E
E
L
K
D
O
O
S
T
P
L
A
N
H
G
E
T
I
P
S
K
N
R
E
D
B
J
H
S
R
P
I
S
L
I
F
T
N
F
I
I
R
P
S
T
R
E
A
H
T
E
G
R
L
G
E
G
S
O
L
F
O
R
C
A
E
A
W
S
P
P
M
A
I
L
G
N
Q
E
E
C
A
J
N
I
In this completed grid, we can read in a circular fashion to obtain lists of words. The remaining letters that don’t lie on any circular loop can be read left-to-right top-to-bottom to get a cluephrase used for Tumbled Tower. The list of words and the cluephrase is as follows:
Large Words
MAC
BRITAIN
JET
BED
Medium Words
JOE
HOUSE
RARE
ENGLISH
CURVE
Small Words
DIPPER
POODLE
BOOMERS
PRINT
PLANET
SPIDER
GOLF
CAPS
WAGE
Cluephrase for Tumbled Tower
ONLY USE BRICK IF ITS SEEN LIGHT FRSDHGLOIKEPBNMAJQC
The final step is to realize that each large word can be prefixed with a synonym of "large" to form a phrase that fits in one of the blanks below. We can do so similarly for the medium words and small words. The blanks all have unique enumerations for matching the phrases. Once all the phrases are placed, we extract via the letters that go in the indicated rectangles. The phrases and extracted letters are as below:
MINIATU(R)E GOLF M(I)NIMUM WAGE BIG MA(C) (H)ALFWAY HOUSE I(T)SY BITSY SPIDER FIN(E) PRINT MEDIUM (R)ARE JUMB(O) JET AVE(R)AGE JOE NORMAL (C)URVE MIDDLE ENGLIS(H) G(R)EAT BRITAIN T(O)Y POODLE BABY BOO(M)ERS DW(A)RF PLANET LI(T)TLE DIPPER K(I)NG SIZE BED SMALL (C)APS
The final cluephrase is therefore RICHTER OR CHROMATIC which clues SCALE.
Author's Notes
I've had the core idea for this puzzle sitting in my puzzles document for a while now. The inspiration for having grids within grids originally came from Patrick's Parabox. Initially, this was going to be a crossword with this type of grid and I had prototyped it as such for our internal puzzle potluck. It felt like the interesting geometry didn't add too much to the crossword solving experience and we were also lacking logic puzzles at the time so I ended up converting this to be a logic puzzle instead.
Originally, the puzzle would just have heptominoes that fit into the grid, but I had a lot of trouble making the solve path logical and interesting. I decided that I needed an extra constraint of some type and landed on inserting some objects into the grid that the heptominoes would have to cover. A bit more brainstorming led me to choosing Akari so that the heptominoes could cover lightbulbs and then I came up with the ambitious idea of reusing the lightbulbs to pare down the heptominoes. It was at this point that I decided to draft the puzzle to be an entangled puzzle.
Designing the extraction for this puzzle came about by brainstorming thematic things to do. One of the most striking features of this grid is that there are squares of various sizes nested together and SCALE happened to be an entangled answer. From there I came up with the wordplay idea of phrases that could be prefixed with a synonym of "large", "medium", or "small".
On the whole, this was a really constrained puzzle to design and I'm really proud of the end result. The exact grid layout was designed so that the number of squares was divisible by 7 and the Akari took quite a bit of work to create so that there were precisely 19 lightbulbs. After that, I started partitioning up the grid into heptominoes, having to make minor adjustments to the Akari I went along. The final set of phrases also needed to have distinct enumeration and that was a bit of challenge too. I'm very happy with the final set of phrases though and particularly enjoyed coming up with ITSY BITSY SPIDER and KING SIZE BED.
