Solving tip - Minesweeper

This is the explaining of my previous Minesweeper post. I wanted to write it a bit earlier.
LMI Beginner Contest has ended 2 weeks ago. Last page of IB contained this link to help the new solvers:
2. Steps to solve minesweeper in EverGreens 1
http://logicmastersindia.com/t/?tid=77

This kind of dividing trick is relatively familiar in Minesweper puzzles. So I thought my set couldn't be full without at least one puzzle that use it.

This was the hardest normal Minesweeper. But I dodn't want to build the whole puzzle only to this trick. So it is mostly solvable without using the dividing.  Hence I don't think that too many people used it.

As I said many Minesweeper puzzle use this trick. Namely:
If you can find distinct regions that use the given number of mines then all remaining cells should be empty.
The main question is: jhow should I know that I have to search regions or solving the puzzle on normal way. Of course there isn't exact answer just some rule of thumb.

This was the 6th puzzle on the contest:

In my opinion in minesweeper puzzles very important the interaction between the clues. So that there there are many clues next to each other ortogonally or at least diagonally. If there are wholes between the clues it is a signed that you can use the dividing trick.

In this case the regions can be the followings:

 

The number of mines in green region is 20, so all white cells are empty.

Moreover, the 6th puzzle contained less mines than the previous puzzles. (30 vs 20)  this is also a sign for using the trick.

Now let's see the posted Minesweeper puzzle. 

In this puzzle the number of mines seems normal, and the clues are close to each other.  But there isn't any trivial starting points. This is the 3rd sign.

So let's try to divide the grid. The sum of subregions should be 30. So try to choose as big numbers as possible, and the regions should be distinct so I tend to choose numbers next to the edge. We can choose both 5s. Then 1 and 2 next to the edge. Then the three 3s in Row 6 and Row 9. And the 2s near to the corner.

 

The sum is 26. We need 4 more. But there is only one  for distinct region. However if we choose the 4 in R5C2 then it has at least 3 more mines. Finally the 4 in R7C8 has 3 green neighbours so it has at least one mine in the white area.

 

We found some regions that contains exactly 30 mines.
So all white cells are empty and the orange regions use the minimal number of mines, so the intersect og green and orange regions are full of mines.

 

 

Now it is a more easier puzzle. With some easy steps such as 1-2 in top-left corner. Or 2 in R9C1 with only 2 empty squares. Or 4 in R4C7.


In this puzzle there wasn't any easy starting point. But sometimes there are some easy steps then it is hard to  continue the solving. In this case you should think about the region-dividing.

Sometimes you can't make regions with the exact number of mines, but there are only some mines on the white area. In this case the regions can help to mark some empty cells or just solve the puzzle.


Rarely the regions work on inverse way. This means that you should find regions which use the minimal number of mines and all remaining cells contain mines.

In this nr.289  puzzle contain only 10 mines, but the clues are all really low. After some basic steps, it is possible to make regions so that the whole white region is totally filled.

nr. 951 - Daily League Sudoku -Tight Fit Killer Sudoku

This sudoku is the combination of Tight Fit Sudoku and Killer Sudoku.
All rules of these two genre are valid. Namely:

• Fill in the grid with digits from 1 to 9, so that each row, column and bolded-line region contains each digit exactly one.
• Each single cell contains exactly one digit, and each cells that divided by a line contains 2 digits; in these cells the smaller number must go above the larger number.
•  The digits within a dotted-line sub-region must be all different.
• The given numbers indicate the sum of digits in the corresponding sub-region.

I hope you will enjoy this funny hybrid sudoku.

nr. 952 - Minesweeper

My Beginner Contest on LMI has just finished. Now I can't write a long summary.

I post a Minesweeper puzzle which is harder than last normal puzzle on the competition.

In the next post I will write about its solving tecqnique. Now here is the puzzle without any comment :)

Rules for Minesweeper

Rules: Minesweeper

Place the given number of mines into the empty cells, so that each digit represents the number
of mines in the 8 neighbouring cells.

nr. 953 - Year of Snake

Normally the Hungarian Puzzle Championship consists of 3 rounds. 2 mix. For instanced Classic and less Classic and a bit special. I made this puzzle in 2011, a combined snake puzzle.

 It was 50 minutes long and 4 people could finish it. Don't forget that the best Hungarian solvers didn't participate, because they made puzzles for WPC.

I tried to construct it so that many partial points are available. I think it was an enjoyable round, at least for those who like snake puzzles :)
The puzzle and its example are found in pdf.
I don't publish the solution of example puzzle this time.

Thanks to Zoltan Nemeth for translating.


This round consists of 6+1 Snake puzzles. The six puzzles in coloured grids can be solved on their own. Solving any two adjacent coloured grids allows for the white area between them to be solved.                                                   
                       
Top left and bottom right puzzles                               
Classic snake                               
"Basic snake rules: Draw a snake into the grid which consists of horizontal and vertical segments, never crosses itself and never touches itself, not even diagonally. The head and tail are given as grey circles. The snake avoids black cells.

Classic snake rules: Numbers around the grid indicate the number of cells occupied by the snake in the given row/column."                               
                       
In the sample, top left and bottom right puzzles are classic snakes.                               
                               
Top centre and bottom centre puzzles                               
Finnish snake                               
Basic snake rules apply. The snake goes through all white circles.                               
                               
In the sample, bottom left puzzle is Finnish snake.                               
                               
Top right and bottom left puzzles                               
Graffiti snake                               
Basic snake rules apply. Number groups around the grid denote the cell groups in the given row/column that the snake does NOT occupy, in the order they appear.                                
                               
In the sample, top right puzzle is Graffiti Snake.                               
                               
White puzzle                               
Minesweeper snake                               
The snakes in the six coloured puzzles are all parts of a giant snake.                               
The giant snake's head and tail are given as grey circles in the middle white zone. It enters and exits the coloured puzzles at the grey circles (i.e. the heads and tails of the small snakes).                               
                               
In other words, the giant snake can cross the dotted boundary lines but not the thick ones.                               
Basic snake rules apply to the giant snake. The no-touch rule applies even if one segment is in a coloured area and the other in a white one. There may be multiple segments of the giant snake in the white area.                               
                               
Numbers written into the black squares denote the number of cells occupied by the snake (out of the 8 surrounding cells connected horizontally, vertically or diagonally).                               
                               
No such minesweeper clues are located adjacent to any of the coloured puzzles, therefore they do not provide information to the small snakes. This applies to both the sample puzzle and the competition puzzle.                       

      
                               
Year of snake in pdf

nr. 954 - Daily League Sudoku - Product Squares Sudoku

 I made this sudoku some month ago. My solving time now is 15 minutes, let's see if anyone can solve it under 5 minutes :)

Rules for Product Squares Sudoku:
Standard sudoku rules apply. Additionally for each gray squares the bottom cells contain a two-digit number which is the product of the numbers in the two upper cells.

For instance if the top numbers are 7-9 or 9-7 the bottom is 6-3 (stricly in this order).

nr. 955 - Mini Sudoku

I made this puzzle for last year's hungarian Sudoku Championship. The original version was too hard, so I added some more extra numbers and signs. The final version was enough easy.

6 player could finish it under 35 minutes.

I post here just the original one. The puzzle is downloadable in pdf.

Since the example is a valid puzzle, as well. I won't publish its solution.
Have fun!


Zoltán Németh translated the rules.

This round consists of nine Sudokus of size 6 that are connected through relational signs. Standard Sudoku rules apply in all these puzzles. Some of the small Sudokus may have a unique solution on their own, while others need neighbouring puzzles' information to be solved.

Relational signs are located between the puzzles, as in the sample. For halved Sudoku, the relational sign should be applied for the digit within the cell even if it is in the half cell away from the sign.

There is no other connection between the puzzles, e.g. the shape of tiling does not need to match between puzzles 4 and 6, even if in the sample they happen to look alike.

1.Top left: Irregular Sudoku

The boxes are not necessarily rectangular.

2. Top centre: Thermometer Sudoku

Starting from the bulb of a thermometer, its digits must strictly increase, although not necessarily by one. E.g. 1,2,4,5 could be a valid thermometer.

3.Top right: Neighbours Sudoku

A dot denotes that the difference between the digits in the two edge adjacent cells is one. All such dots are given. In other words, where there is no dot, the difference is not one.

4. Centre left: Half Box Sudoku

The grid is divided into areas of 3 cells each. Pair them to establish areas of 6 cells each such that these areas can serve as boxes for Sudoku rules perspective, allowing no digit to repeat. Each box has to be connected.

5. Centre: Diagonal Sudoku

No digit can repeat in either of the main diagonals. There are no boxes given.

6. Centre right: Tripod Sudoku

The boxes are not given and have to be restored. Wherever three segments of the boxes' boundaries form a T-junction, a dot is placed. There are no junctions where four such segments meet.

7. Bottom left: Kropki Sudoku

White dots denote that the difference between two adjacent digits is one. Black dots denote that one of the digits is twice the other. Wherever there are no dots, the two digits do not satisfy either criterion. There may be a white or a black dot between a 1 and a 2.

8. Bottom centre: Arrows Sudoku

Digits in a circle equal to the sum of digits on any arrow starting from that circle.

9. Bottom right: Halved Squares Sudoku

Squares that are halved also contain a digit in one of the halves; the other half remains empty. A number in one half of a cell does not belong to the area that contains the other half of the same cell.

 

Mini sudoku.pdf