## Island - a very elegant logic puzzle

For fans of all other kinds of logic puzzles

### Island - a very elegant logic puzzle

I was first introduced to this puzzle genre from Para's blog: puzzleparasite-dot-blogspot-dot-com

Para wrote:
Island is a genre developed by Naoki Inaba.

Fill in some cells to form a single island. The cells with numbers are part of this island. The numbers indicate how many unnumbered cells can be reached from that cell by moving horizontally or vertically. Numbered cells block access.

Such simple rules for such an intriguing game! Personally I think it is more fun than Nurikabe and Heyawake, two very well known binary puzzles "in the market".

Here is a 6x6 example puzzle provided in Para's blog:

For those uninspired, I will include a walkthrough in the next post to indicate how to solve these puzzles using "pure logic".

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

This is the walkthrough for the example puzzle above:

Walkthrough for the 6x6 example puzzle: Show
@ = land, # = water

Code: Select all
`2.3...........4......5...........5.7`

Consider the land for R1C1=2:
R2C1 <> #, = @ (or the land for R1C13=[2,3] will be isolated from the rest)
--> R3C1 & R2C2 <> @, = # (or the land for R1C1=2 will be isolated from the rest)
--> R1C2 = @
--> R2C3 <> #, = @ (or the land for R1C13=[2,3] will be isolated from the rest)

Code: Select all
`2@3...@#@...#.4......5...........5.7`

Consider the land for R6C6=7:
R6C5 <> #, = @ (or the land for R6C6=7 will be isolated from the rest)
--> R5C6 <> #, = @ (or the land from R6C5 will have area 7, too big for R6C4=5)
--> R5C5 <> @, = # (or the land from R5C5 will have area 7, too big for R6C4=5)
--> The land from R5C6 has area 6, too big for any other number
--> R34C6 = @, R4C5 = #

Code: Select all
`2@3...@#@...#.4..@...5#@....#@...5@7`

Consider the land for R6C5=5:
R5C4 <> #, = @ (or the land for R6C5=5 will be isolated from the rest)
--> R5C3 <> #, = @ (or the rest of the land for R4C4=5 will have area 4, too big for R3C3=4)
--> R4C3 <> @, = # (or R3C3=4 will limit total land from R35C4+R4C3 to be 3, too small for R4C4=5)

Code: Select all
`2@3...@#@...#.4..@..#5#@..@@#@...5@7`

R6C5=5: the land from R5C4 has area 4
R4C4=5: the land from R3C4 has area 1
--> R3C4 = @, R2C4 & R3C5 = #
R1C3=3: R1C4 = @, R1C5 = #
R6C6=7: R1C6 & R2C56 = @
R3C3=4: R34C2 = @, R4C1 & R5C2 = #
R6C5=5: R6C23 = @, R56C1 = #

Code: Select all
`2@3@#@@#@#@@#@4@#@#@#5#@##@@#@#@@5@7`

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

Here are two of the easiest Island puzzles from Para's blog, just so you can get a feel of them:

I will post the walkthroughs for these puzzles later, that is after I finish writing them!

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

This is my complete walkthrough for the first 8x8 puzzle above:

Complete walkthrough for 8x8 puzzle #1: Show
Code: Select all
`.3.2.........1.2.4.1.........4.34.3.........3.4.1.2.........1.2.`

R2C6=1: R1C6,R2C5 <> @, = # --> R3C7 = #
R3C4=1: R3C5,R4C4 <> @, = # --> R2C3 = #
R7C1=1: R8C1 <> @, = # --> R6C2 = #
R8C5=1: R8C4 <> @, = # --> R7C6 = #

Code: Select all
`.3.2.#....#.#1.2.4.1#.#....#.4.34.3......#..3.4.1.2..#..#..#1.2.`

R1C4=2: R1C3 <> #, = @
R2C8=2: R3C8 <> #, = @
R8C7=2: R7C7 <> #, = @
R1C2=3: R2C2 <> #, = @
R4C8=3: R4C7 <> #, = @

Code: Select all
`.3@2.#...@#.#1.2.4.1#.#@...#.4@34.3......#..3.4.1.2..#@.#..#1.2.`

R7C3=2: R67C4 cannot be both @ (or the water R1C6+R23C5+R45C4+R68C3+R7C2 will divide the island)
Also R7C45 cannot be both @ (too big for R8C5=1)
R7C3=2: R6C3 <> #, = @
R5C3=3: R4C3+R5C2 cannot be both # (or the water R1C6+R23C5+R4C34+R56C2+[R6C1/(R7C2+R8C1)] will divide the island)
R5C3=3: at least one @ from [R4C3/R5C2] and one @ from R6C3
--> R5C3=3: R5C4 <> @, = # (or the water R1C6+R235C5+R468C4+[R7C4/R7C5] will divide the island)
--> R6C4 <> #, = @ (or the water R1C6+R23C5+R4568C4+[R7C4/R7C5] will divide the island)

Code: Select all
`.3@2.#...@#.#1.2.4.1#.#@...#.4@34.3#.....#@@3.4.1.2..#@.#..#1.2.`

R7C3=2: R7C24+R8C23 = #
R7C1=1: R6C1 = @
R5C3=3: R4C3 <> @, = # (or the water R1C6+R23C5+R4C4+R3C3+R45678C2 will divide the island)
R5C3=3: R5C2 = @, R4C2 = #
R5C1=4: R34C1 = @, R2C1 = #
R1C2=3: R1C1 = @
R3C2=4: R3C3 = @
R3C4=1: R2C4 = #
R1C4=2: R1C5 = @

Code: Select all
`@3@2@#..#@###1.2@4@1#.#@@###.4@34@3#....@#@@3.4.1#2#.#@.####1.2.`

R6C5=3: R5C5 <> @, = # (or the water R156C6+R2347C5+R8C4 will divide the island)
R68C5=[3,1]: R7C5 <> @, = # (or the water R1678C6+R235C5+R4C4 will divide the island)
R68C5=[3,1]: R68C6 = @, R5C6 = #
R8C7=2: R78C8 = #
R4C68=[4,3]: R3C6+R4C5+R5C7 = @, R5C8 = #
R6C7=4: R6C8 = #
R2C6=1: R2C7 = #
R2C8=2: R1C8 = @, R1C7 = #

Code: Select all
`@3@2@##@#@###1#2@4@1#@#@@###@4@34@3###@#@#@@3@4#1#2###@#####1@2#`

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

This is my complete walkthrough for the second 8x8 puzzle above:

Complete walkthrough for 8x8 puzzle #2: Show
Code: Select all
`8.....8.....8...8..........8..8.........8..........8.........8..`

R1C1=8: R1C23+R2C1 = @, R2C2 = # (or the land for R1C1=8 with area 8 will be isolated from the land for R8C6=8)
R3C1=8: R3C2+R4C1 = @, R4C2 = # (or both the land for R13C1=[8,8] with area 7 will be isolated from the land for R8C6=8)
R1C7=8: R1C6 <> #, = @ (or the land for R1C7=8 with area 7/8 will be isolated from the land for R6C1=8)

Code: Select all
`8@@..@8.@#..8...8@......@#.8..8.........8..........8.........8..`

R1C1=8: the land from R1C2 with area 7 cannot touch R3C2 (too big for R3C1=8)
--> the land from R1C2 with area 7 must touch R2C5=8 (or max area = 4 < 7)
--> R2C5=8 must have one @ with area 1
R2C5=8: R2C4 cannot be @ with area 1 (or max area for the land from R1C2 = 2 < 7)
--> R2C5=8: R3C5 = @, R3C46+R4C5 = #

Code: Select all
`8@@..@8.@#..8...8@.#@#..@#.8#.8.........8..........8.........8..`

R4C4=8: R4C3+R5C4 = @, R5C3 = # (or the land for R4C4=8 with area 8 will be isolated from the land for R3C1=8)
R4C4=8: R3C3 <> #, = @ (or the land from R5C4 with area 7 will be isolated from the land for R3C1=8)
R1C1=8: R2C3 <> @, = # (or the land from R1C2 with area 7 will be too big for R3C1=8)
R1C1=8: R2C6 <> #, = @ is part of the land from R1C2 with area 7 (or max area for the land from R1C2 = 6 < 7)
R1C7=8: the land from R1C8 has area 1 --> R1C8 = @, R2C8 = #
R3C1=8: the land from R4C1 has area 4 --> R5C12+R6C2 = @, R6C3+R7C2 = #
R6C1=8: the land from R7C1 has area 4 --> R7C1+R8C123 = @, R7C3+R8C4 = #

Code: Select all
`8@@..@8@@##.8@.#8@@#@#..@#@8#.8.@@#@....8@#.....@##8....@@@#.8..`

R7C4=8: R6C4+R7C5 = @, R6C5 = # (or the land for R7C4=8 with area 8 will be isolated from the land for R1C7=8)
R4C4=8: the land from R5C4 has area 5 --> R5C56 = @
R7C4=8: the land from R7C5 has area 3 --> R7C6 = @, R6C6 = #
R8C6=8: R8C7 = @, R7C7 = # (or the land for R8C6=8 with area 8 will be isolated from the land for R1C7=8)
R7C4=8: the land from R7C5 has area 3 --> R8C5 = @
R8C6=8: the land from R8C7 has area 5 --> R678C8 = @

Code: Select all
`8@@..@8@@##.8@.#8@@#@#..@#@8#.8.@@#@@@..8@#@##.@@##8@@#@@@@#@8@@`

R4C4=8: R4C6 = @, R5C7 = # (or max area from R8C7 = 4 < 5)
R4C7=8: the land from R3C7/R4C8 has area 3 --> R3C78+R4C8 = @, R2C7+R5C8 = #
R1C1=8: the land from R1C2 has area 7 --> R1C45+R2C4 = @
R8C6=8: the land from R8C7 has area 5 --> R6C7 = @

Code: Select all
`8@@@@@8@@##@8@##8@@#@#@@@#@8#@8@@@#@@@##8@#@##@@@##8@@#@@@@#@8@@`
Last edited by simon_blow_snow on Thu Mar 29, 2012 2:58 pm, edited 1 time in total.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

simon_blow_snow wrote:I was first introduced to this puzzle genre from Para's blog: puzzleparasite-dot-blogspot-dot-com

Para wrote:
Island is a genre developed by Naoki Inaba.

Fill in some cells to form a single island. The cells with numbers are part of this island. The numbers indicate how many unnumbered cells can be reached from that cell by moving horizontally or vertically. Numbered cells block access.

Such simple rules for such an intriguing game! Personally I think it is more fun than Nurikabe and Heyawake, two very well known binary puzzles "in the market".

Here is a 6x6 example puzzle provided in Para's blog:

For those uninspired, I will include a walkthrough in the next post to indicate how to solve these puzzles using "pure logic".

In R4 (4th row from top), why is it that not all of the cells are filled in?
As R4C4 (4th row from the top/4th column from left) cointains a 5 so all cells of R4 could be reached from there.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Island - a very elegant logic puzzle

dyitto wrote:In R4 (4th row from top), why is it that not all of the cells are filled in?
As R4C4 (4th row from the top/4th column from left) cointains a 5 so all cells of R4 could be reached from there.

I don't quite understand that question?

R4C4=5 means there are 5 land cells directly connected to R4C4, they are R3C4, R5C34 & R6C23.

All other land cells are indirectly connected to R4C4, that is R4C4 can only reach them via a path through other numbered cells, e.g. R6C5 through R6C4=5.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

I just realised why dyitto/evert had trouble understanding the rule. The wording (as scribed from Para's blog) was a bit confusing.

It should be rephrased as below:

I wrote:
Fill in some cells to form a single island.
The cells with numbers are part of the land on this island.
The numbers indicate how many unnumbered land cells are directly connected to the corresponding cells (in the manner of polyominos).
Numbered cells block direct connections.
Water cells block all connections.

However, with so many words the elegancy of the original puzzle description is lost.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

Now it's clear to me, thanks!
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Island - a very elegant logic puzzle

I managed to solve the first one, although I didn't write a walk-through or check yours - currently lack of time for that.
Very nice puzzle and something really new
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Island - a very elegant logic puzzle

dyitto wrote:I managed to solve the first one, although I didn't write a walk-through or check yours - currently lack of time for that.
Very nice puzzle and something really new

Congratulations!

I find this puzzle genre appealing because the rules feel the most "natural" to me (e.g. without the quirky "2x2" rule as in Nurikabe or the "spanning 3 rooms" rule as in Heyawake). It works around 2 central concepts (connectivity and area) which are both very intuitive to most.

Here are two more from Para's blog, with a slightly higher difficulty than the two above:

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

Here is my complete walkthrough for the third 8x8 puzzle:

Complete walkthrough for 8x8 puzzle #3: Show
Code: Select all
`1.2.........6.4.5..........4..3..2..4..........6.4.4.........4.2`

R1C1=1: R1C2 <> @, = # (or the land for R1C13=[1,2] will be isolated)
--> R1C1=1: R2C1 = @, R2C2 = #
R3C1=5: the land from R3C2/R4C1 has total area 4
--> R3C1=5: R3C23 <> #, = @ (or max land area from R3C2/R4C1 = 3 < 4)
R5C2=2: R4C2 <> @, = #
R1C3=2: R2C3 = #, R1C4 = @ must touch R2C5=6

Code: Select all
`1#2@....@##.6.4.5@@......#.4..3..2..4..........6.4.4.........4.2`

R3C1=5: the land from R3C2 cannot have area 4
(or the land for R13C1=[1,5] together with R1C3+R2C5+R4C4=[2,6,4] or R4C4=4 will be isolated)
--> R3C1=5: R4C1 <> #, = @
R3C1=5: R5C1 <> @, = # (or the land for R13C1+R5C2=[1,5,2] will be isolated)

Code: Select all
`1#2@....@##.6.4.5@@.....@#.4..3.#2..4..........6.4.4.........4.2`

R1C3=2: R23C4 cannot be both @, must have at least one #
R2C5=6: the land from R2C6/R3C5 has total area 4
--> R2C5=6: R3C5 <> #, = @ (or the land for R1C3+R2C57=[2,6,4] will be isolated)
R3C1=5: R4C3 = @, R3C4+R5C3 = #
R4C4=4: R5C4 = @, R4C5+R6C4 = #

Code: Select all
`1#2@....@##.6.4.5@@#@...@#@4#.3.#2#@4......#...6.4.4.........4.2`

R2C5=6: the land from R3C5 cannot have area 4 (or the land for R1C3+R2C57=[2,6,4] will be isolated)
--> R2C5=6: R3C6 <> @, = #
--> R2C5=6: R1C67+R2C6 = @, R1C58 = #
R1C3=2: R2C4 = @
R2C7=4: R3C7 = @, R23C8 = # (or the land for R1C3+R2C57=[2,6,4] will be isolated)

Code: Select all
`1#2@#@@#@##@6@4#5@@#@#@#@#@4#.3.#2#@4......#...6.4.4.........4.2`

R5C2=2: R6C2 = @ is part of a land of area 2
R7C2=4: R8C234 cannot be all @, must have at least one #
--> R7C3 <> #, = @ (or the land for R57C2 = [2,4] will be isolated)
R5C2=2: R6C1 = @, R6C3+R7C1 = #

Code: Select all
`1#2@#@@#@##@6@4#5@@#@#@#@#@4#.3.#2#@4...@@##...6#4@4.........4.2`

R6C8=6: max land area from R5C8 = 2 (R4C7=3)
R6C8=6: max land area from R7C8 = 2 (R8C8=2)
--> R6C8=6: R6C7 <> #, = @ (max land area from R57C8 = 4 < 6)
R8C8=2: R7C7 <> @, = # (or the land from R67C7 will be too big for R8C8=2)
--> R8C8=2: R7C8+R8C7 = @

Code: Select all
`1#2@#@@#@##@6@4#5@@#@#@#@#@4#.3.#2#@4...@@##..@6#4@4..#@.....4@2`

R6C8=6: the land from R5C8/R6C7 has total area 5
--> R6C8=6: R5C7 <> @, = # (or max land area from R5C8/R6C7 = 2 < 5)
R6C8=6: the land from R6C7 cannot have area 4 or 5 (too big for R5C5+R8C6=[4,4])
--> R6C8=6: R45C8+R6C6 = @
R4C7=3: R4C6 = #

Code: Select all
`1#2@#@@#@##@6@4#5@@#@#@#@#@4##3@#2#@4.#@@@##.@@6#4@4..#@.....4@2`

R6C8=6: the land from R6C7 with area 3 must touch R5C5=4
--> R8C6=4: R7C6 <> @, = #
R8C6=4: R7C5+R8C45 = @, R6C5+R8C3 = #
R5C5=4: R5C6 = @
R7C2=4: R8C2 = @, R8C1 = #

Code: Select all
`1#2@#@@#@##@6@4#5@@#@#@#@#@4##3@#2#@4@#@@@###@@6#4@4@##@#@#@@4@2`

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

Here is my complete walkthrough for the fourth 8x8 puzzle:

Complete walkthrough for 8x8 puzzle #4: Show
Code: Select all
`....1..48..6................2..68..5................3..66..4....`

R1C5=1: R1C6 <> @, = # (or the land for R1C5=1 will be isolated)
R1C8=4: the only reachable numbered cell for the land for R1C8=4 is R4C8=6
--> R1C8=4: the land bridging R14C8=[4,6] cannot have area 2 (or the land for R1C8=4 has max area = 3 < 4)
R4C8=6: the only reachable numbered cells for R4C8=6 are R1C8+R4C5+R7C8=[4,2,6]
--> R4C8=6: the land for R4C8=6 must touch R7C8=6 (or the land for R14C8=[4,6] and/or R4C5=2 will be isolated)
--> R4C8=6: the land for R4C8=6 must only touch R1C8=4 (with area 3 or 4) and R7C8=6 (with area 2 or 3)
R7C8=6: the only reachable numbered cells for the land for R7C8=6 are R4C8+R7C5=[6,3]
--> R7C8=6: the land for R7C8=6 must touch both R4C8+R7C5=[6,3] (or the land for R147C8=[4,6,6] will be isolated)
--> R7C8=6: the land for bridging R7C58=[3,6] must be 2 NOT 3 (or the land for R14C8+R7C58=[4,6,3,6] will be isolated)
--> R7C58=[3,6]: R7C67 = @, R68C67 = #
--> R47C8=[6,6]: R5C78+R6C8+R8C8 = @, R4C7+R5C6 = #
--> R14C8=[4,6]: R13C7+R23C8 = @, R2C7+R3C6 = #

Code: Select all
`....1#@48..6..#@.....#@@....2.#68..5.#@@.....##@....3@@66..4.##@`

R7C5=3: the land for R7C5=3 must touch R8C4=4 (or the land for R14C8+R7C58=[4,6,3,6] will be isolated)
--> R7C5=3: the land from R7C4/R8C5 has exactly one @, R6C5 = #
R8C4=4: the land from R8C3 has area 3 and must touch R8C1=6 (or the land for R14C8+R7C58+R8C4=[4,6,3,6,4] will be isolated)
R8C1=6: R7C2 <> @, = # (or the land for R8C1=6 will have area 6, too big for R8C4=4)
--> R8C1=6: R6C12+R7C13+R8C23 = @, R5C2+R6C3+R7C24 = #
--> R8C4=4: R8C5 = @

Code: Select all
`....1#@48..6..#@.....#@@....2.#68#.5.#@@@@#.###@@#@#3@@66@@4@##@`

R4C5=2: the land from R4C4/R5C5 has max area 2
R5C4=5: R45C3 <> #, = @ (or the land for R5C4=5 has max area 4 < 5)
R4C5=2: R4C4 <> @, = #
R5C1=8: R4C1 = @ leads to a piece of land with area 5
--> R5C1=8: R3C1 <> #, = @ (or the land for R14C8+R5C14+R7C58+R8C14=[4,6,8,5,3,6,6,4] will be isolated)

Code: Select all
`....1#@48..6..#@@....#@@@.@#2.#68#@5.#@@@@#.###@@#@#3@@66@@4@##@`

R5C14=[8,5]: R4C2 <> #, = @ (or the land for R5C4=5 has max area 4 < 5)
--> R5C14=[8,5]: R3C23+R5C5+R6C4 = #
R4C5=2: R4C6 <> @, = # (or the land for R4C5=2 will be isolated)
--> R14C5=[1,2]: R1C4+R3C45 = @, R1C3+R2C56 = #
R2C4=6: R1C2+R2C23 = @, R1C1 = #

Code: Select all
`#@#@1#@48@@6###@@##@@#@@@@@#2##68#@5##@@@@#####@@#@#3@@66@@4@##@`

Note this one requires an extensive conceptual analysis at the very start without any actual placement, which is the characteristic of a thoughtful puzzle at a decent level of difficulty. The remaining Island puzzles from Para's blog (which I will post soon) all have this characteristic.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

These are the remaining 3 puzzles from Para's blog (so far):

8x8 Island #5

8x8 Island #6

9x9 Island #1

Good luck solving them!

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Island - a very elegant logic puzzle

In this link you can find the puzzles made by Naoki Inaba, who came up with the genre.

http://inabapuzzle.com/honkaku/island.html
Para

Posts: 46
Joined: 20 February 2007

Next