Four Winds

Rules and Tips for standard puzzle types, and their variants
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pinkagape
Posts: 121
Joined: Mon 30 Apr, 2012 4:11 pm

Four Winds

Post by pinkagape » Wed 18 Nov, 2020 10:09 pm

Here are the rules of Four Winds, from the WPF website:

Draw one or more lines from each numbered cell so that each number indicates the total length of lines that are drawn from that cell, excluding the cell itself. Lines are either horizontal or vertical and connect the centers of adjacent cells without crossing or overlapping each other and the given numbers.

For me, the key is that cells all need to be joined to the numbers with straight lines, joining exactly the number of cells as the number given. The two main things that I will look for is cells which can only join to one given number, and numbers which only have so many possible cells that they can join.

Here is an example puzzle.

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The 6 in the corner only has two directions to go in. If it went all the way to the edge of the grid to the left, it would still need to go two cells down. Similarly, if it went all the way to the edge of the grid down, it would still need to go two cells left. Therefore it must go at least two cells down and two cells left.

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The 7 is a pretty big number and now only have seven cells left to join to in straight lines, so they must all join to the 7.

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The 6 can now only go three cells left, so it must go at least three cells down.

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The 4 now only has four cells left to join to in straight lines, so they must all join to the 4.

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The 6 still has two choices to join to, but the blank cell on the top row can only join to the 6, so it must do so.

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Similar logic dictates how the remaining cells must join to the only numbers they can reach.

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pinkagape
Posts: 121
Joined: Mon 30 Apr, 2012 4:11 pm

Re: Four Winds

Post by pinkagape » Wed 18 Nov, 2020 10:09 pm

Here is an example for you to try.

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GarethMoore
Posts: 1252
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Re: Four Winds

Post by GarethMoore » Sat 21 Nov, 2020 2:07 am

pinkagape wrote:
Wed 18 Nov, 2020 10:09 pm
The two main things that I will look for is cells which can only join to one given number, and numbers which only have so many possible cells that they can join.
It should probably be noted that the first rule only applies if the sum of the numbers is equal to the number of empty squares, which is often but certainly not always the case.

Mephisto
Posts: 85
Joined: Tue 18 Jan, 2011 12:28 pm

Re: Four Winds

Post by Mephisto » Sat 21 Nov, 2020 4:06 pm

@Gareth: Not necessarily. IMHO if a cell remains empty, it is not reachable at all. Or can you post a contra-example (which has only one solution)?

pinkagape
Posts: 121
Joined: Mon 30 Apr, 2012 4:11 pm

Re: Four Winds

Post by pinkagape » Sat 21 Nov, 2020 4:18 pm

GarethMoore wrote:
Sat 21 Nov, 2020 2:07 am
pinkagape wrote:
Wed 18 Nov, 2020 10:09 pm
The two main things that I will look for is cells which can only join to one given number, and numbers which only have so many possible cells that they can join.
It should probably be noted that the first rule only applies if the sum of the numbers is equal to the number of empty squares, which is often but certainly not always the case.
In the Beginners competition, there will be no empty cells left over, because I’ve never seen one with any empty squares when I wrote the puzzles. It’s a good idea for the Advanced...

GarethMoore
Posts: 1252
Joined: Thu 24 Jun, 2010 9:27 pm
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Re: Four Winds

Post by GarethMoore » Mon 23 Nov, 2020 1:11 pm

Mephisto wrote:
Sat 21 Nov, 2020 4:06 pm
@Gareth: Not necessarily. IMHO if a cell remains empty, it is not reachable at all. Or can you post a contra-example (which has only one solution)?
The following puzzle has only one solution, and yet the square marked 'x' is reachable but not visited in the solution. It also has a second square not visited in the solution.
Clipboard01.png
Clipboard01.png (7.32 KiB) Viewed 54 times

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