## Sunday, 22 June 2014

This is the next part of my Radar tutorial.
The description of first trick, and the solution of example puzzle has already posted.

Now let's see the second trick, and a new practise puzzle.

If there are a 2 and 3 clue next to each other there is no rectangle that can part of both rows.
Similarly if there are a 3 and 4 clue next to each other there is no rectangle that can part of both rows.

Because of every rectangle is at least 2 units wide. If a clue is 2 then there is only one 2-wide rectangle in that row. Similarly if a clue is 3 then there is only one rectangle in the corresponding row.
So a 2-wide and a 3-wide rectangle cannot be same.

Similarly a 4 clue can be a simple 4 or 2+2. It cannot part a 3-wide rectangle.

First I check if there is anywhere these kind of clues and I draw a bolded line between the two rows. It is a wall. These walls divide the grid into subregions.

In the next practise puzzle it is needed to use this trick and the previous one, too.
The biggest number is 9 in a 12x12 grid. There are 3 empty squares in that row, which seems too many.
But for instance there is a wall between R3 and R4.And it means that R3C7 or R4C7 is empty or both of them. These walls make it possible for the puzzlemaker to use a bit smaller numbers for starting.

Next time I will show the solving steps of this puzzle.

## Friday, 20 June 2014

### nr. 945 - Daily League Sudoku - Product Sudoku

My next puzzle in DLS series is much harder than the previous one.
This kind of sudoku is enjoyable for me, although the starting steps are quite boring. i.e. counting the prime factors of each clue.
If you like the math puzzle, but this one is too big for you, just visit my old site for easier Magic Squares with products.

Rules for Product Sudoku:
Follow classic sudoku rules. At some intersections of two crossing grid lines, a number is given. This number show the product of digits in the four adjacent cells.

## Saturday, 14 June 2014

### How to solve Radar? I.

I show a possible solving line for nr. 946 - Radar puzzle.

First I marked the trivial empty squares (rows where the clue is 0), and I marked the same clues next to the edge or empty rows.

Then let's check the biggest clues. The are two 9s. C10 seems better, becase there are two marked empty cells while in R3 there is only one.

So C10 contain10 unmarked cells and 9 are filled. We can make the simple deductions.

Now we can use the trick. R1C10 and R9C10 are also filled.
So in C10 there remains 2 unfilled cells, R4C10 and R12C10.
Because of the 7 in R4  R4C10 cannot be empty.
We can fill the whole C10, then easy to fill the whole right side.

Now lets check the biggest clues again. Try to find rows/columns where there are N empty cells and N-1 are filled.
These are R3 and R11-R12.

Now we can use again the trick. And mark some cells in C1.
Then there are some simple deductions again such as R3C6 cannot be empty because then it is not possible to finish R2.

So finishing this puzzle isn't too hard.

But I want to show one more thing.

In C1-C2 there are 7s. It is an odd clue so there is at least one rectangle with odd width in this column. It can be just 3 width.

And clues in R9 and R10 are same, so it cannot be in the bottom part. Just in the up part.
Clues in R1 and R2 are also same. So it can be just in R1-R2-R3.

This is the way how it is possible to use the same clues trick.

## Wednesday, 11 June 2014

This is the first part of the (mini) series that will show the tricks of Radar puzzle type.
Let's see the first trick.

If the first and second clue is same on any side, than the first and second row is totally same.
The same is true, if there is 0 among the clues. And its neighbour and its second neighbour is same.

This is a simple consequence of the rule that every rectangles is at least 2 cells width.
So if there is a shaded cell in first row it will continue in the second. And the two clues are same, so there is no more shaded cells in the second row.

Here is an example which use only this trick.
For instance if R3C1 is shaded then it is trivial that R3C2 is shaded too.
Because of the trick the inverse is also true.
This is not trivial, but it is not a too difficult consequnce.

Another example is that if R3C2 is empty then it is trivial that R3C1 is empty too.
But the inverse is also true.
If R3C1 is empty then R3C2 is empty too.

First I check both sides of the clue and mark this pattern to not forget to use this trick.
In this puzzle there are 4 places where 1st and 2nd clue are same. But R6 and R7 won't give any extra informations because of the zeros.
Next time I will show the first steps of this puzzle.

## Sunday, 8 June 2014

Radar is one of my favourite puzzles. It's a well-known genre, but it's not especially popular recently.  Hence I will publish some puzzles, and I will share some solving tips.

I was thinking when I can say that this is a trick of the puzzle types.
I think  anything that more then a simple deduction is trick or pattern.

Such as in a Yin and Yang puzzle when in a 2x2 area there are 3 white circles then the 4th is black is just a simple deduction. But the edge connection is a trick.
Of course it is consequence of rules, so it is a logical deduction, but not a simple deduction.
My first 4 Yin and Yang puzzle on the Beginner Contest were solvable without any trick, but it is more faster if you use the tricks in trivial puzzle too.

Today I publish the 0th puzzle of the series. I call it 0th puzzle because it is solvable with simple deductions.

For example if there are N empty cells in a row, and it is required to fill N-1, then it is a simple deduction that the 2nd cell from the side cannot be empty.
Or if the clue is 3, then there is only one cloud in that row which is 3 cells width.

Normally I like creating 10x10 puzzles without given cloud parts. But when I make a trickless one, it is better to give some elements and to use a bigger size.

## Friday, 6 June 2014

### nr. 948 - Daily League Sudoku - Quadruple Sudoku

This is a familiar sudoku variant. I think it is one of the easiest where there is no given numbers.

If you want to solve this sudoku online you can do it tomorrow at SudokuCup.

Follow classic sudoku rules. At some intersections of two crossing grid lines, a set of four numbers is given. These numbers must be placed in the four adjacent cells.

## Wednesday, 4 June 2014

### nr. 949 - Yajilin

If you missed my Yajilin puzzles, here is one. It has medium difficulty. Enjoy!

Rules for Yajilin

## Monday, 2 June 2014

### nr. 950 - Battleships

Simple (?) Battleships puzzle with only few clues, and with some kind of antisymmetric pattern.

Rules for Battleships