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Sudoku techniques

Sudoku grid consists of 81 squares divided into nine columns marked a through i, and nine rows marked 1 through 9. The grid is also divided into nine 3x3 sub-grids named boxes which are marked box 1 through box 9.

Scanning techniques

The easiest way starting a Sudoku puzzle is to scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square. The scanning technique is fast and usually sufficient to solve easy puzzles all the way to the end. The scanning technique is also very useful for hard puzzles up to the point where no further progress can be made and more advanced solving techniques are required. Here are some ways of using scanning techniques:

1. Scanning in one direction:

In our first example we will focus on box 2, which like any other box in Sudoku must contain 9. Looking at box 1 and box 3 we can see there are already 9s in row 2 and in row 3, which excludes the two bottom rows of box 2 from having 9. This leaves square e1 as the only possible place into which 9 can fit in.

2. Scanning in two directions:

The same technique can be expanded by using information from perpendicular rows and columns. Let’s see where we can place 1 in box 3. In this example, row 1 and row 2 contain 1s, which leaves two empty squares in the bottom of box 3. However, square g4 also contains 1, so no additional 1 is allowed in column g. This means that square i3 is the only place left for 1.

3. Searching for Single Candidates:

Often only one number can be in a square because the remaining eight are already used in the relevant row, column and box. Taking a careful look at square b4 we can see that 3, 4, 7 and 8 are already used in the same box, 1 and 6 are used in the same row, and 5 and 9 are used in the same column. Eliminating all the above numbers leaves 2 as the single candidate for square b4.

4. Eliminating numbers from rows, columns and boxes:

There are more complex ways to find numbers by using the process of elimination. In this example the 1 in square c8 implies that either square e7 or square e9 must contain 1. Whichever the case may be, the 1 of column e is in box 8 and it is therefore not possible to have 1 in the centre column of box 2. So the only square left for 1 in box 2 is square d2.

5. Searching for missing numbers in rows and columns:

This method can be particularly useful when rows (and columns) are close to completion. Let’s take a look at row 6. Seven of the nine squares contain the numbers 1, 2, 3, 4, 5, 8 and 9, which means that 6 and 7 are missing. However, 6 cannot be in square h6 because there is already 6 in that column. Therefore the 6 must be in square b6.

Analyzing techniques

As Sudoku puzzle levels get harder you will find the simple scanning methods described above are not enough and more sophisticated solving techniques must be used. Hard puzzles require deeper logic analysis which is done with the aid of pencilmarks. Sudoku pencilmarking is a systematic process writing small numbers inside the squares to denote which ones may fit in. After pencilmarking the puzzle, the solver must analyze the results, identify special number combinations and deduce which numbers should be placed where. Here are some ways of using analyzing techniques:

1. Eliminating squares using Naked Pairs in a box:

In this example, squares c7 and c8 in box 7 can only contain 4 and 9 as shown with the red pencilmarks below. We don’t know which is which, but we do know that both squares are occupied. In addition, square a6 excludes 6 from being in the left column of box 7. As a result the 6 can only be in square b9. Such cases where the same pair can only be placed in two boxes is called Disjoint Subsets, and if the Disjoint Subsets are easy to see then they are called Naked Pairs.

2. Eliminating squares using Naked Pairs in rows and columns:

The previous solving technique is useful for deducing a number within a row or column instead of a box. In this example we see that squares d9 and f9 in box 8 can only contain 2 and 7. Again we don’t know which is which, but we do know that both squares are occupied. The numbers which remain to be placed in row 9 are 1, 6 and 8. However, 6 can’t be placed in square a9 or in square i9, so the only possible place is square c9.

3. Eliminating squares using Hidden Pairs in rows and columns:

Disjoint Subsets are not always obvious to see at first sight, in which case they are called Hidden Pairs. If we take a very close look at the pencilmarks in row 7 we can see that both 1 and 4 can only be in square f7 and square g7. This means that 1 and 4 are a Hidden Pair, and that square f7 and square g7 cannot contain any other number. Using the scanning technique we see that 7 can only be in square d7.

4. Eliminating squares using X-Wing:

The X-Wing technique is used in rare situations which occur in some extremely difficult puzzles. Scanning column a we see that 4 can only be in square a2 or square a9. Similarly, 4 can only be in square i2 or square i9. Because of the X-Wing pattern where boxes are in the same row (or column), a new logic constraint occurs: it is obvious that in row 2 the 4 can only be either in square a2 or in square i2, and it cannot be in any other square. Therefore 4 is excluded from square c2, and square c2 must be 2.

http://www.conceptispuzzles.com

How to Play Chess

Chess rules are relatively easy to learn, I would say that they are somewhere around a medium level of difficulty. What makes the game so complex and beautiful at the same time is the huge number of possible moves at any point during the game.

What you need

Chess is an abstract battle board game played between two opponents.
The ingredients required to play the game are:

• a square shaped board divided into 64 squares alternatively colored in black and white;
• 32 pieces: 16 white pieces for one player and 16 black pieces for the other player.

The chess board is placed in between the two opponents in such a manner that each of them has a black square on the left corner of the board. Both players start off with an identical set of 16 pieces: 8 pawns , 2 rooks , 2 knights , 2 bishops , a queen and a king .

In the table below are shown the 6 types of pieces along with their names and symbols. I should point out that the name and thus the symbol of the pieces is different from one language to another.

Chessman	Name	Symbol
	The king	K
	The queen	Q
	The rook	R
	The bishop	B
	The knight	N
	The pawn	P

Chess board setup

Chess rules

Each player must move one piece at a time. So, in fact, the game is played in a succession of moves. Each piece moves after a certain rule form one square to another and the game always starts with the player having the white pieces, making the first move. A piece can also capture an enemy piece according to certain rules. Some pieces are more important than others depending on their range of action and their value; for example: the queen is the strongest piece on the board because it has the greatest range of action while the king is the most important piece because it is the main piece targeted by the enemy attack. There are times when a move implies the movement of two pieces: when capturing, castling or promoting a pawn; for example when a player captures a piece he takes that piece outside the board and move his own piece in its place.

The purpose of the game

The game revolves around attacking the other side's king. When a king is under the threat of being captured it is said that the king is in check (usually the side attacking the king announce this by saying 'check' but this is not imposed by the rules). When a king is in check it must be moved otherwise it risks being captured (many people don't know this but the king can be captured).

The objective of each player is to checkmate his opponent. That means bringing the enemy king in such a position that when attacked it has no available square on which to move. When a player checkmates his opponent king he wins the game.

While the game evolves both players develop their positions by making various moves and capturing various pieces. This means that the number of pieces will diminish along the game. As you will see in the following articles, because of this, the game's priorities will change along its duration. The rules will remain the same but the objectives will be slightly different. This is why the game can be divided into three different parts depending on the number and the position of the pieces: the opening, the middle game , the end game.

There are times when neither of both sides can win the game. In this case the game ends at equality and it is said to be a draw(a tie). This situations are quite frequent especially when both players are around the same level of expertise. The game doesn't need to be balanced in order for the game to end a draw. This is thoroughly discussed at draw and stalemate.

If the game reaches to a point where the advantage of on side is obvious or a draw is inevitable, the game could be ended if both players agree on the result of the game.

Chess notation

If you want to better understand the chess rules you will have to study various games. In order to do that you will have to know how the games are recorded. There are more than one official ways of writing down a game. We will use in this site only one type of notation, the most common one : algebraic chess notation. The notation is quite simple. In order to realize what went where, each square has its own coordinate. Each row (called a rank) of the board has a number from 1 to 8 and each column (called a file) a letter from a to h, each of those directions starting from the left corner on the side of the white pieces. This way each square, sometimes called a field, has its own unique coordinate (made of the intersection of a line with a column) as shown in the board below. This subject is covered at notation.

In the above paragraph I talked about directions (the rows 1 - 8 and the columns a to h). I should point out that beside those type of directions we also have another type : the diagonals. The diagonals are made of squares of the same color. Look at the following example: through the b3 passes two diagonals d1-a4 and a2-g8 (marked in red), the rank 3 and the file b (marked in green).The diagonal a1-h8 is called the main black diagonal and h1-a8 is called the main white diagonal.

Some other chess rules

There are also some conduct rules you should know about:

• Don't pressure your opponent in moving to fast. Remember: this is a game of patience!
• If you moved a piece you can't take back your move.
• If you touched a piece than you must move that piece. If you want to arrange a piece that might be a little bit outside a square than you must announce your opponent.
• If you moved a piece on a square and you didn't take your hand off it, you can move it on another square.

If your opponent lets you, you can take back your move or move a piece different that the one you touched.

This are all the chess rules you need to know for now. There are other rules concerning how the game is played in official competitions that you can find on the world chess federation site, but I suggest you learn them after you know how to play chess. And in order to know how to do that you need to know the chess rules concerning how each piece moves and captures. You can read about that by going to the next article.

http://www.chessguru.net/chess_rules/

How To Play: Blackjack

Blackjack is a one-on-one game between player and banker. The rules are surprisingly easy, but the pace is fast, so it really tests a player’s skill and memory, which is why it is so popular around the world.

The key aim in Blackjack is to have more total points than the banker with a maximum of 21. The banker deals two cards to each player and one to himself. Players look at the sum of their cards and decide whether to stand, hit, split, or double down. A player can take cards until he senses the total is sufficient or if the total points exceeds 21, which is a bust. When all players have drawn their cards, the banker takes his second card and then hits for himself.

Calculation of points

In Blackjack, the ace scores either one point or 11 points; the number cards from 2 to 9 score at face value; and 10, jack, queen and king score 10 points.

Drawing

Players can draw a card with any point total, while the banker must draw cards for all totals less than or equal to 16.

Blackjack

If the sum of the first two cards equals 21, it’s called a blackjack. It’s possible to achieve 21 with more than two cards, though this combination is not called a blackjack.

Splitting Pairs

If a player has two cards of the same value, such as two aces or two 9’s, he can split them into two different hands.

Doubling Down

When a player receives the initial two cards, he has the option of doubling his bet. After doubling, a player can only draw once.

Take Insurance

If the banker’s first card is an ace, the players can make a supplementary bet called “insurance”. If in the end the banker gets Blackjack, the player who has taken insurance can win twice that supplementary bet.

Five Dragons

As long as the banker’s first card is not an ace, a player with 5 cards totalling no more than 21 points can demand to be paid half his bet. However, this is not the standard practice in Macau casinos.

Commonly Used Gestures

Hit: Use your fingers to tap lightly in front of your cards or brush towards you
Stand: With palm facing down, shake your hand from left to right over your cards (without touching them)
Pass: Slide your fingers on the table from left to right.