# World's Smallest Logic Puzzles

### by Alex Gotsis, Alex Pei, and Ivan Wang

We are presented with sets of grids and alphabetized names of Nikoli-style logic puzzles. As the title of the puzzle suggests, each grid is a trivialized or degenerate version of a logic puzzle (for example, a 1x1 Sudoku which solves to a single 1). Our goal is to match up logic puzzles to grids and fill them in. Two helpful resources for the exact rules are https://www.nikoli.co.jp/en/puzzles/ and http://www.cross-plus-a.com/puzzles.htm.

Each set of grids also contains connectors. The double-edge represents equality, while the double-edge with a line represents inequality. Using this, we can find a unique assignment and solution to the grids. See the Appendix for a walkthrough of each puzzle.

Once we’ve associated the logic puzzles, we can extract a cluephrase by indexing the given numbers into the puzzle name and reading in order from left to right. This solves to PLACE BLANK GRIDS TAKE NEIGHBORS.

Upon closer inspection, we should notice that each set of grids (when completely solved) has one logic puzzle whose solve state is entirely blank. In the given order, this matches up exactly with the 8 blanks (of sizes 1x1 and 2x2) in the grid of letters at the bottom.

By putting the blank grids in order in the appropriate place and highlighting the adjacent neighbor(s) from the logic puzzle, we can find the final answer hidden within the grid, CHAOS DOMAIN.

Hover over a subpart or puzzle box to highlight the corresponding entry.

Subpart 1
Subpart 2
Subpart 3
Subpart 4
Subpart 5
Subpart 6
Subpart 7
Subpart 8
B
L
A
C
K
W
A
S
P
I
C
E
H
O
C
K
E
Y
S
T
R
A
W
P
O
L
L
M
O
H
S
S
C
A
L
E
I
N
S
I
D
E
O
U
T
D
R
O
P
S
A
F
E
B
L
U
E
M
O
O
N
O
R
G
A
N
P
I
P
E
G
N
A
W
S
O
F
F
B
U
N
N
Y
H
O
P

## Authors' Notes

This was an incredibly degenerate puzzle to write (for more than one definition of the word). Inspiration for this puzzle came from World’s Largest Logic Puzzle.

We authors had fairly pedantic conversations about the rules of these logic puzzles in ways that were certainly never intended.

## Appendix

Below, we provide possible solve paths for each set of grids, as well as some key points from each logic puzzle.

Hover over a puzzle name or puzzle box to highlight the corresponding entry.

#### Subpart 1

1. Masyu and Linesweeper both need to form complete loops; by contradiction, they can't be in the middle grid.
2. Linesweeper doesn't have a circle, so Masyu goes on top.
3. Tatamibari is the only remaining puzzle with bars.
4. Tatamibari forces full loops on other puzzles.
5. Clouds must be blank (it needs 2x2 to be black).
6. This forces Clouds to the rightmost 1x1.
7. Hamle is the remaining cell; it must be a black with 0 indicating 0 moves.
(2)
|
(9)
0
(4)
P
L
A

#### Subpart 2

1. Castle Wall needs to form a complete loop and does not contain circles, so it must be the 2x2.
2. Therefore Castle Wall is just a 2x2 loop.
3. The bottom left must now be Dotchi-Loop because none of the other puzzles allow circle + loop.
4. Top right cell of Dotchi cannot be part of a loop, so it must be blank or a black circle.
5. Right-most must be Douieru based on shape, with a white or double-circle in the top-left.
6. No other grids have a double-circle, so it must be a white circle.
7. Fobidoshi must be the 1x1 above, since Dosun-Fuwari requires >=1 black circle, and Tren has no circles.
8. Dosun-Fuwari must be the bottom with a black circle connecting to Dotchi-Loop.
9. Tren is the remaining 1x1, which is white because blocks must be of size 1x2 or 1x3, and numbers must appear in blocks.

#### Subpart 3

1. Both Simple Loop and Suraromu require a complete loop.
2. If Simple Loop is the bottom, the rightmost cell is a corner path, which is a contradiction.
3. Suraromu must go on bottom, with a ⓪ in that location, forcing Kurotto.
4. Similarly, in the top left, Simple Loop must have a black cell in the bottom right.
5. This forces Canal View, the only remaining puzzle with a black.
6. By process of elimination, Tents is the last 1-grid.
7. It must be blank because the number of tents equals the number of trees, and there isn't room for both.
(1)
(5)
(4)
(3)
L
A
N
K

#### Subpart 4

1. Doppelblock requires a square grid and 2 blacks in each row/col, so it must be the 2x2.
2. This means the top 1x1 must be black, and constrains the rightmost grid.
3. LITS requires >4 squares per region, so it must be the rightmost, and it must have only 1 region.
4. Rectslider and Santoitchi are the only remaining puzzles with numbers. But numbers in Santoitchi require a white region of size 3, so the 2x1 must be Rectslider with 2 blacks.
5. LITS must be an L shape by the white and black constraints.
6. Santoitchi and Nonogram remain. Santoitchi must be black because whites must be in a region of size 3.
7. Nonogram is thus the remaining white.
(5)
(1)
0
(2)
G
R
I

#### Subpart 5

1. Calcudoku is the only puzzle with a 4+.
2. This puts a 4 in the middle grid.
3. The middle grid can't be Sudoku or Sukoro since 4 is too high; it can't be Snake Pit, since a snake with 4 cannot be a 2x2 cell.
4. The middle grid must be Hidato by process of elimination.
5. The right grid cannot be Sudoku (which is a square grid), so it must be Sukoro or Snake Pit.
6. If the right grid is Sukoro, the only possible number that satisfies equality to Hidato is 1. But that cell can't have 1 neighbor with a number, since two 1's would be adjacent. Thus the right grid is Snake Pit with 2.
7. Sudoku and Sukoro are thus the 1-grids
8. Hidato's top-left must be a 1, since Sudoku/Sukoro don't support larger numbers.
9. Sukoro must be blank since a single cell has no neighbors.
(3)
(1)
1
(3)
(5)
2
1
2
2
4+
4
4
3
D
S
T
A

#### Subpart 6

1. Norinori must have 2x1 black but not 2x2 black; it can't be in 2x2 because of self-equality.
2. Norinori can't be left 2x1 or it causes b ≠ b, so it's the rightmost 2x1.
3. Tilepaint is the only puzzle with a number outside; by Norinori it must be black.
4. Middle can't be all black (same reason as above), so it must be Rukkuea with a 1b or wb.
5. Shikaku is the remaining possible 1x1 which must be a 1.
6. Tetroid by process of elimination is the 2x2 all white.
(2)
?
(4)
(6)
1
1
(1)
K
E
N
E

#### Subpart 7

1. Arofuro is the only puzzle with a naked number. It can't be the 2x1 grid in the middle because otherwise it would duplicate the 1.
2. Sashikabe can't be that grid either since it needs an L shape, so Gaidoaro has to be there.
3. This links to Star Battle via a star since Gaidoaro needs a star (the link can't be Yokibunkatsu because of region size).
4. If Arofuro were the right arrow grid, then its top right cell is either a number (rejected for equality since no more naked number puzzles) or an arrow (rejected since Sashikabe, the remaining arrow puzzle, cannot be a 1x1 arrow).
5. Therefore Sashikabe is the right grid with black in the top right.
6. Now we know the top right grid must be black.
7. But a degenerate Arofuro can only be black, so top right must be Arofuro.
8. This leaves Yokibunkatsu as top middle. It has to be white since it's not a star.
(4)
(4)
(1)
I
G
H

#### Subpart 8

1. Kakurasu must be top-right since it's the only puzzle that has numbers around edges.
2. Only two puzzles have circles, Nanbaboru or Kurodoko, so they are the left two grids.
3. Left can't be Kurodoko since all white cells have to be connected and black cells cannot touch. This leaves Nanbaboru which puts a 2 in the circle.
4. Sto-stone must be in the top grid, as neither Ringring nor Shakashaka have borders.
5. Ringring must either be a 1x1 black or a 2x2 loop, but the latter would violate the self-edge, so it must be the 1x1.
6. Since blacks can't touch over borders in Sto-stone, this forces a checkerboard pattern. With the edge to Ringring's black, the pattern must be black/white/white/black.
7. This forces Kurodoko to have whites along the right edge.
8. Shakashaka is forced to be all white in the last 2x2 because of 3 equals, and the requirement that whites must form a rectangle.
1
?
?
1
2
1
(6)
(4)
(1)
(1)
B
O
R
S