Four Winds
Four Winds
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.
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.
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.
The 6 can now only go three cells left, so it must go at least three cells down.
The 4 now only has four cells left to join to in straight lines, so they must all join to the 4.
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.
Similar logic dictates how the remaining cells must join to the only numbers they can reach.
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.
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.
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.
The 6 can now only go three cells left, so it must go at least three cells down.
The 4 now only has four cells left to join to in straight lines, so they must all join to the 4.
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.
Similar logic dictates how the remaining cells must join to the only numbers they can reach.
Re: Four Winds
Here is an example for you to try.

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Re: Four Winds
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.
Re: Four Winds
@Gareth: Not necessarily. IMHO if a cell remains empty, it is not reachable at all. Or can you post a contraexample (which has only one solution)?
Re: Four Winds
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 wrote: ↑Sat 21 Nov, 2020 2:07 amIt 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.

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Re: Four Winds
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.
Re: Four Winds
Lovely example Gareth
Here are two more examples of "full" Four Winds like in the Beginners December competition.
Here are two more examples of "full" Four Winds like in the Beginners December competition.