## Introducing Sanaku

Post puzzles for others to solve here.

### Introducing Sanaku

The goal is to connect all the islands(Circles) by drawing a series of bridges(Lines) between the islands. The bridges must follow certain criteria:
• Bridges must not cross each other.
• They may only run horizontally, vertically, or diagonally (45 degrees)
• At most one bridge connects a pair of islands.
• The number of bridges connected to each island must match the number on that island.
• The bridges must connect the islands into a single connected group.
• Some bridges are given initially, the goal is to find the remaining bridges

Note: Dotted gray lines show possible bridges

Here's a sample with the solution:

networkpuzzle.png (68.65 KiB) Viewed 149 times

And here's a sample for you to solve:
Sample001.png (147.65 KiB) Viewed 149 times
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sanaku

Is this correct?

my solution: Show
Code: Select all
`1 . 1 . 1 - 3 - 3 - 3 . 1 - 3 - 2| / . . . / . / . / . \ . / . / .4 . 1 - 4 . 1 . 2 . 1 - 3 . 3 - 1| \ . / | . . / . . . . . / . . .1 . 3 . 1 . 1 . 2 . 1 . 2 . 1 - 2. / . . . . . / . \ . \ . \ . . |1 . 1 - 3 - 2 . 2 . 2 . 4 - 4 - 2. . . / . . . / . \ | / . \ . \ .1 - 2 . 2 . 1 . 2 . 5 - 1 . 2 . 1. . . / | . . / . \ | . . . | . .1 . 1 . 2 - 3 . 2 . 2 . 2 - 5 - 1. \ . . . . | . | \ . / . . | \ .2 . 2 . 1 - 2 . 1 . 2 . 1 - 3 . 2| \ . \ . . . . . . . . . / . / .1 . 2 - 4 . 1 - 3 - 3 . 1 . 2 - 2. . . / . \ . / . . | \ . . . . |1 - 3 - 1 . 3 - 1 . 1 . 2 - 2 - 2`

The same without the dots:

Code: Select all
`1   1   1 - 3 - 3 - 3   1 - 3 - 2| /       /   /   /   \   /   /  4   1 - 4   1   2   1 - 3   3 - 1| \   / |     /           /      1   3   1   1   2   1   2   1 - 2  /           /   \   \   \     |1   1 - 3 - 2   2   2   4 - 4 - 2      /       /   \ | /   \   \  1 - 2   2   1   2   5 - 1   2   1      / |     /   \ |       |    1   1   2 - 3   2   2   2 - 5 - 1  \         |   | \   /     | \  2   2   1 - 2   1   2   1 - 3   2| \   \                   /   /  1   2 - 4   1 - 3 - 3   1   2 - 2      /   \   /     | \         |1 - 3 - 1   3 - 1   1   2 - 2 - 2`

That would have been so much easier with a printed copy, but no printer around. That's why I can't really be sure if it has mistakes or not. No guesswork was needed.

SpAce

Posts: 1903
Joined: 22 May 2017

### Re: Introducing Sanaku

These are fun puzzles, but I've seen them before ... in a "Daily Puzzle" tear-off calendar.

"9 x 9" is nice !
blue

Posts: 894
Joined: 11 March 2013

### Re: Introducing Sanaku

SpAce wrote:Is this correct?

my solution: Show
Code: Select all
`1 . 1 . 1 - 3 - 3 - 3 . 1 - 3 - 2| / . . . / . / . / . \ . / . / .4 . 1 - 4 . 1 . 2 . 1 - 3 . 3 - 1| \ . / | . . / . . . . . / . . .1 . 3 . 1 . 1 . 2 . 1 . 2 . 1 - 2. / . . . . . / . \ . \ . \ . . |1 . 1 - 3 - 2 . 2 . 2 . 4 - 4 - 2. . . / . . . / . \ | / . \ . \ .1 - 2 . 2 . 1 . 2 . 5 - 1 . 2 . 1. . . / | . . / . \ | . . . | . .1 . 1 . 2 - 3 . 2 . 2 . 2 - 5 - 1. \ . . . . | . | \ . / . . | \ .2 . 2 . 1 - 2 . 1 . 2 . 1 - 3 . 2| \ . \ . . . . . . . . . / . / .1 . 2 - 4 . 1 - 3 - 3 . 1 . 2 - 2. . . / . \ . / . . | \ . . . . |1 - 3 - 1 . 3 - 1 . 1 . 2 - 2 - 2`

The same without the dots:

Code: Select all
`1   1   1 - 3 - 3 - 3   1 - 3 - 2| /       /   /   /   \   /   /  4   1 - 4   1   2   1 - 3   3 - 1| \   / |     /           /      1   3   1   1   2   1   2   1 - 2  /           /   \   \   \     |1   1 - 3 - 2   2   2   4 - 4 - 2      /       /   \ | /   \   \  1 - 2   2   1   2   5 - 1   2   1      / |     /   \ |       |    1   1   2 - 3   2   2   2 - 5 - 1  \         |   | \   /     | \  2   2   1 - 2   1   2   1 - 3   2| \   \                   /   /  1   2 - 4   1 - 3 - 3   1   2 - 2      /   \   /     | \         |1 - 3 - 1   3 - 1   1   2 - 2 - 2`

That would have been so much easier with a printed copy, but no printer around. That's why I can't really be sure if it has mistakes or not. No guesswork was needed.

Printable ones available at http://www.parspicks.com/Sanaku/
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sanaku

blue wrote:These are fun puzzles, but I've seen them before ... in a "Daily Puzzle" tear-off calendar.

"9 x 9" is nice !

Are you sure you've seen it before? I've designed it myself, I'd like to know if I've reinvented the wheel
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sanaku

koushanejad74 wrote:Are you sure you've seen it before? I've designed it myself, I'd like to know if I've reinvented the wheel

I'm sure.
Circled numbers, dotted lines, the "all connected", and "no crossing lines" rules ... everything the same.

I remember being disapponted in one of the puzzles.
One of the dotted lines that "should have been there", was removed to give the puzzle a unique solution.

I remember a technique that was needed sometimes:

Code: Select all
`           /          /     A -- 5 -- B     \  /|\  /      \/ | \/      /\ | /\     /  \|/  \    C -- 4 -- DThe "5" has 6 possible connections.There can't be connections to both C and D, or the "4" would become impossible.Conclusion: you can darken the 4 lines from the "5", that don't go to C or D.[ Added: and darken the lines from "4" to C and D ]`

The C-4-D line was almost always at the edge of the puzzle.

Sorry,
Blue.

Added: To be honest, I think the "all connected" rule was only mentioned when it was really necessary to use it.

I think they were in one or more of the "365 Brain Puzzlers" calendars, from the years when it was "by Mark Danna & Fraser Simpson".
Mark Danna "retired" after the 2016 calendar, I see.

https://www.amazon.com/365-brain-puzzlers/s?k=365+brain+puzzlers
https://www.amazon.co.uk/365-Brain-Puzzlers-2016-Official/dp/0761183663
https://www.barnesandnoble.com/w/2015-mensa-365-brain-puzzlers-page-a-day-calendar-mark-danna/1118136636
Last edited by blue on Fri Aug 02, 2019 3:24 pm, edited 1 time in total.
blue

Posts: 894
Joined: 11 March 2013

### Re: Introducing Sanaku

I hadn't seen this exact variant before. I've only played the normal type (Hashi?) with double bridges (and without diagonals, dotted lines and givens). The same logic seems to work on both, so not much different from that either. Fun puzzles anyway, like blue said. I used to buy cheap sudoku booklets just to solve the few specials (mainly bridges, slitherlinks, and killers), often never even touching the garbage vanilla sudokus in them.

blue wrote:I remember being disapponted in one of the puzzles.
One of the dotted lines that "should have been there", was removed to give the puzzle a unique solution.

Oh. Is that why the dotted lines are there in the first place? I thought they were just a nuisance instead of an extra constraint. Then again, if they're almost never used as a constraint, then they probably shouldn't even be one (to disallow ugly kludges like that). Either way, I'd probably prefer to get rid of those damn lines, at least in a puzzle like this example with such short distances. I guess they could help with long diagonals where it might be harder to see the exact 45 degree angle, but even then I'd just draw faint aiming lines across every diagonal instead of marking only possible connections (spotting those should be part of the solving). For aiming purposes they're hardly needed for the vertical and horizontal directions at all.

SpAce

Posts: 1903
Joined: 22 May 2017

### Re: Introducing Sanaku

http://cross-plus-a.com/puzzles.htm
It's almost like Hashiwokakero, and something like Korekutokonekuto, Ichimaga.
creint

Posts: 129
Joined: 20 January 2018

### Re: Introducing Sanaku

SpAce wrote:Oh. Is that why the dotted lines are there in the first place? I thought they were just a nuisance instead of an extra constraint. Then again, if they're almost never used as a constraint, then they probably shouldn't even be one (to disallow ugly kludges like that).

I only saw the one puzzle, where the "ugly kludge" had been used.
I would draw a thin perpendicular across the lines that could be eliminated.
Having the rest of them there, made it easy to count up what was left, looking for "singles"
blue

Posts: 894
Joined: 11 March 2013

### Re: Introducing Sanaku

blue wrote:
SpAce wrote:Oh. Is that why the dotted lines are there in the first place? I thought they were just a nuisance instead of an extra constraint. Then again, if they're almost never used as a constraint, then they probably shouldn't even be one (to disallow ugly kludges like that).

I only saw the one puzzle, where the "ugly kludge" had been used.
I would draw a thin perpendicular across the lines that could be eliminated.
Having the rest of them there, made it easy to count up what was left, looking for "singles"

Dotted lines are there just to help the player, not a constraint; I can easily remove 'em or add something in the description to clearly explain what they are for
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sanaku

Just posted a more challenging sample here: sanaku-challenging-sample-t36309.html
koushanejad74

Posts: 75
Joined: 31 July 2019

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