Kakuro CD Rom 256 Page Book Rules 1,000 Puzzles & Solutions

KaKuro CD

by Eureka 1,000 Puzzles and Solutions

UNUSUAL ALPHA NUMERIC GAME

of a square showing three equal size

squares across and down the board.

KAKURO– The new Brain Bending Additive

Puzzle Game taking the world by storm!

now that you have mastered Sudoku

Are you ready to become a Kakuro Master?

which is An Interesting alpha Numeric Game?

If you survive d Sudoku this game of Kakuro will drive you crazy faster than a speeding bullet.

A game for all ages and no luck or knowledge of mathematics, to enable you to win.

Kakuro is a game of logic played with the use of the CD Rom

CD ROM Features: Unlimited puzzle variation

Play as often as you like!

Play on Screen or board. Five levels of difficulty, easy, harder, difficult, and diabolical and Killer Sudoku

Multi-level ‘undo feature

Beat the clock and record fastest time.

Save or print unfinished games- solve at your leisure, solutions may be printed

Handy hint feature (just in case)

Easy to Play.

You Don't Have To Be Good

At Maths To Play Kakuro

You've probably entered a bookstore to see a table

overflowing with partially gridded numbers

pictured on the covers of numerous books titled

'Sudoku and Kakuro'

you believed you would have to be good at maths to play these games.

Kakuro is a great mental workout.

Keeps your mind sharp and mentally active.

It's great fun, addictive and inexpensive hobby.

Very much like Cryptic Crossworks Puzzles.

For those people who do not claim to be mental giants,

but believe they are more logical than anything else,

here is a puzzle that will test your skills of logic.

Are you

WARNING THIS PUZZLE GAME IS ADDICTIVE,

You may find less time sleeping and more time solving

If

KaKuro CD Rom 256 Page Book

by Eureka 1,000 Puzzles and Solutions

UNUSUAL ALPHA NUMERIC GAME

of a square showing three equal size

squares across and down the board.

KAKURO– The new Brain Bending Additive

Puzzle Game taking the world by storm!

now that you have mastered Sudoku

Are you ready to become a Kakuro Master?

which is An Interesting alpha Numeric Game. If you survive d Sudoku this game of Kakuro will drive you crazy faster than a speeding bullet.

A game for all ages and no luck or knowledge of mathematics, to enable you to win.

Kakuro is a game of logic played with the use of the CD Rom

CD ROM Features: Unlimited puzzle variation

Play as often as you like!

Play on Screen or board. Five levels of difficulty, easy, harder, difficult, diabolical and Killer Sudoku

Multi-level ‘undo feature

Beat the clock and record fastest time.

Save or print unfinished games- solve at your leisure, solutions may be printed

Handy hint feature (just in case)

Easy to Play.

No messy rubbing out if a mistake is made.

Book features 1, 000 Kakuro Puzzles with Solutions and Rules

Remember there is only one unique solution for each puzzle.

Kakuro is a puzzle that combines elements of sudoku and kakuro. The hardest ones, however, can take hours to crack.

Kakuro, Hot on the heels of Sudoku now heralding KAKURO. The new Fiendish and Highly Additive Puzzle Game from Japan.

It's called Cross Sums in the USA, Kakuro in the UK, and Kakro in Japan.

What is it? A fun, entertaining and highly addictive puzzle game that will make you go crazy...

System requires: - 500 Mhz, 32mb RAM, Windows 98/ME/2000/XP, 3D accelerated graphics card, DirectX 9.

Kakuro solving techniques

Cross reference

Find 2 intersecting runs and compare the clue number combinations for each. Any values which appear in the combinations for both runs are candidates for the square on which the runs intersect.

In this example, the "down" clue is 6, which has only 1 combination (1+2+3), whereas the "across" clue 20, has 4 combinations (3+8+9, 4+7+9, 5+6+9 and 5+7+8). However, the only common number in both sets of combinations is 3, therefore the intersection square must be 3.

Combo reference

This technique works by picking a run and performing a cross reference on every square along it, weening out combinations until you have only 1 left.

In this example we take the "across" run 12, which has the combinations (3+9, 4+8 and 5+7).

The first square (A) intersects a run with the combinations (1+4 and 2+3). Since neither 5 nor 7 appear in these, we can discount the 5+7 combination from the first run. However, this still leaves us with the combinations (3+9 and 4+8).

The second square (B) intersects with a run which has only 1 combination (7+9), and since the (4+8) combination shares no common numbers we can remove it, leaving only 1 combination for our original run (3+9).

Knowing that this run has only 1 combination, we can now fill in this section of the puzzle.

Filled areas

In this example, we can deduce that the square outside of the blank 2x2 area shown must be a 3; we can do this using the filled area technique.

Firstly, add together all the "across" clues (4+3=7). Then add together all the "down" clues (4+6=10). Now work out the difference between those totals (10-7=3) and that will be the value of the square which is not in the 2x2 area.

Eliminating duplicates

Using this technique you can eliminate any number combinations which would lead to certain patterns of numbers (as shown in the examples).

The pattern shown the examples, with the numbers on the top row being the same as the bottom row (albeit in a different order), can never occur anywhere on a valid Kakuro board as it would lead to more than 1 solution.

If you swapped the top and bottom rows in the examples, the numbers would still add to the same clues, but would yield a different solution to the puzzle.

Bearing in mind that a Kakuro puzzle has only 1 solution, you should avoid any numbers which would create the patterns seen here.

Kakuro or Kakkuro (Japanese:) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword. Kakuro puzzles are regular features in most, if not all, math-and-logic puzzle publications in the United States. Dell Magazines came up with the original English name Cross Sums and other names such as Cross Addition have also been used, but the Japanese name Kakuro, abbreviation of Japanese kasan kurosu, addition cross) seems to have gained general acceptance and the puzzles appear to be titled this way now in most publications. The popularity of Kakuro in Japan is immense, second only to Sudokuamong Nikoli's famed logic-puzzle offerings.[1]

Standard play and terminology

The canonical Kakuro puzzle is played in a grid of filled and empty cells — "black" and "white", respectively — usually 16×16 in size, but these dimensions can vary widely. Apart from the top row and left most which is entirely black the grid, just like a crossword, is divided into "entries" — orthogonal lines of white cells — by the black cells. The black cells themselves — possibly barring those in a cluster — are not entirely solid but rather contain a diagonal slash from upper-left to lower-right and a number in one or both halves, such that each horizontal entry has a number in the black half-cell to its immediate left and each vertical entry has a number in the black half-cell immediately above it. These numbers, continuing the borrowed crossword terminology, are commonly called "clues".

The object of the puzzle is to insert a digit from 1 to 9 inclusive into each white cell such that the sum of the numbers in each entry matches the clue associated with it and that no digit is duplicated in any entry. It is that lack of duplication that makes creating Kakuro puzzles with unique solutions possible, and which means solving a Kakuro puzzle involves investigating combinations more, compared to Sudoku in which the focus is on permutations.

History

Killer sudokus were already an established variant of sudoku in Japan by the mid 1990s, where they were known as "samunamupure." The name stemmed from a Japanized form of the English words "sum number place." Killer sudokus were introduced to most of the English-speaking world by The Times in 2005.

Traditionally, as with regular sudoku puzzles, the grid layout is symmetrical around a diagonal, horizontal or vertical axis. This is a matter of aesthetics, though, rather than obligatory: many Japanese puzzle-makers will make small deviations from perfect symmetry for the sake of improving the puzzle. Other puzzle-makers may produce entirely assymmetrical puzzles.

Terminology

• cell — a single square that contains one number in the grid
• row — a horizontal line of 9 cells
• column — a vertical line of 9 cells
• nonet — a 3x3 grid of cells, as outlined by the bolder lines in the diagram above
• cage — the grouping of cells denoted by a dotted line or by individual colours. It is a convention of killer sudokus that there are no duplicate numbers within a cage, with the implication that no cage can include more than 9 cells.

Rules

The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met:

• Each row, column, and nonet contains each number exactly once.
• The sum of all numbers in a cage must match the small number printed into it.
• No number can appear more than once in a cage.

In 'Killer X', an additional rule is that each of the long diagonals contains each number once.

Solving strategies

Fewest possible combinations

Generally the problem is best tackled starting from the extreme sums — cages with the largest or the smallest sums. This is because these have the fewest possible combinations. For example, 3 cells totalling 23 can only be 6, 8 and 9.

In the early stages of the game, the most common way to begin filling in numbers is to look at such low-sum or high-sum cages that form a 'straight line'. As the solver can infer from these that certain numbers are in a certain row or column, he can begin 'cross-hatching' across from them.

The 45 rule

A further technique can be derived from the knowledge that the numbers in all rows, all columns and all nonets add up to 45. By adding up the cages and single numbers in a particular row, column or nonet, the user can deduce the result of a single cell. If the cell calculated is within the nonet itself it is referred to as an 'innie'; conversely if the cell is outside the nonet it is called an 'outie'. Even if this is not possible, advanced players may find it useful to derive the sum of two or three cells, then use other elimination techniques (see below for an example of this). The '45' technique can also be extended to calculate cells from two or more connected rows, columns or (most commonly) nonets, in which case the solver has to refer to the multiples of 45 accordingly.

Initial analysis of the sample problem

Fewest possible combinations

The two cells in the top left must be 1+2. The 3 cells to the right totaling 15 cannot therefore have either a 1 or a 2, so they must be either 3+4+8, 3+5+7 or 4+5+6.

The two vertical cells in the top left of the top right nonet cannot be 2+2 as that would mean duplicates, so they must be 1+3. The 1 cannot be in the top line as that conflicts with our first 2 cells therefore the top cell of this pair is 3 and the lower cell 1. This also means the 3 cell cage 15 to the left cannot contain a 3 and so is 4+5+6.

Similarly the neighbouring 16 must be 9+7.

The four cells in the top right cannot include both 1 & 3, nor both of 9 & 7; If any of 1, 3, 7 or 9 are present then they must be the lone square in the nonet below. Therefore these 4 cells are one of 1+2+4+8, 1+2+5+7 or 2+3+4+6.

The 2 cells in the middle of the left edge must be either 1+5 or 2+4. And so on.

45

Looking at the nonet on the left hand side in the middle, we can see that there are three cages which do not cross over into another nonet; these add up to 33, meaning that the sum of the remaining two cells must be 12. This does not seem particularly useful, but consider that the cell in the bottom right of the nonet is part of a 3-cage of 6; it can therefore only contain 1, 2 or 3. If it contained 1 or 2, the other cell would have to contain 11 or 10 respectively; this is impossible. It must, therefore, contain 3, and the other cell 9.

Duplicate cell ambiguity

By convention in Japan, killer sudoku cages do not include duplicate numbers, even if they crossed nonets. When The Times first introduced the killer sudoku in 2005, however, the newspaper did not make this rule explicit. Even though the vast majority of sudoku puzzles followed the rule anyway, English-speaking solvers scratched their heads over appropriate solving strategies given the ambiguity. Within a month, though, the Times clarified the rule, and now the world standard is no duplicates within cages.

It is easiest to determine the combinations within large cages by means of complements. The table for 6 cell cages is the complement of the 3 cell table adding up to "45 - listed value"; similarly the 7 cell table complements the 2 cell table. An 8-cell cage is of course missing only one digit (45 - the sum of the cage).

External links

• Too good for Fiendish? Then try Killer Su Doku - article in The Times
• Killer Su Doku - some tips for solvers
• Killer Sudoku solving tips and example work through of a puzzle
• JC's Killer Sudoku - solving techniques
• DJApe's Killer Sudoku - solving tips
• SudoCue Killer solving guide
• Sudoku Tiger Killer Solving Guide

You Don't Have To Be Good

At Maths To Play Kakuro

You've probably entered a bookstore to see a table

overflowing with partially gridded numbers

pictured on the covers of numerous books titled 'Sudoku and Kakuro'

you believed you would have to be good at maths to play these games.

Kakuro is a great mental workout.

Keeps your mind sharp and mentally active.

It's great fun, addictive and inexpensive hobby.

Very much like Cryptic Crossworks puzzles.

For those people who do not claim to be mental giants,

but believe they are more logical than anything else,

here is a puzzle that will test your skills of logic.

Are you

WARNING THIS PUZZLE GAME IS ADDICTIVE,

You may find less time sleeping and more time solving

If-

digit (45 - the sum of the cage).

History

Killer sudokus were already an established variant of sudoku in Japan by the mid 1990s, where they were known as "samunamupure." The name stemmed from a Japanized form of the English words "sum number place." Killer sudokus were introduced to most of the English-speaking world by The Times in 2005.

Traditionally, as with regular sudoku puzzles, the grid layout is symmetrical around a diagonal, horizontal or vertical axis. This is a matter of aesthetics, though, rather than obligatory: many Japanese puzzle-makers will make small deviations from perfect symmetry for the sake of improving the puzzle. Other puzzle-makers may produce entirely assymmetrical puzzles.

Terminology

• cell — a single square that contains one number in the grid
• row — a horizontal line of 9 cells
• column — a vertical line of 9 cells
• nonet — a 3x3 grid of cells, as outlined by the bolder lines in the diagram above
• cage — the grouping of cells denoted by a dotted line or by individual colours. It is a convention of killer sudokus that there are no duplicate numbers within a cage, with the implication that no cage can include more than 9 cells.

Rules

The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met:

• Each row, column, and nonet contains each number exactly once.
• The sum of all numbers in a cage must match the small number printed into it.
• No number can appear more than once in a cage.

In 'Killer X', an additional rule is that each of the long diagonals contains each number once.

Solving strategies

Fewest possible combinations

Generally the problem is best tackled starting from the extreme sums — cages with the largest or the smallest sums. This is because these have the fewest possible combinations. For example, 3 cells totalling 23 can only be 6, 8 and 9.

In the early stages of the game, the most common way to begin filling in numbers is to look at such low-sum or high-sum cages that form a 'straight line'. As the solver can infer from these that certain numbers are in a certain row or column, he can begin 'cross-hatching' across from them.

The 45 rule

A further technique can be derived from the knowledge that the numbers in all rows, all columns and all nonets add up to 45. By adding up the cages and single numbers in a particular row, column or nonet, the user can deduce the result of a single cell. If the cell calculated is within the nonet itself it is referred to as an 'innie'; conversely if the cell is outside the nonet it is called an 'outie'. Even if this is not possible, advanced players may find it useful to derive the sum of two or three cells, then use other elimination techniques (see below for an example of this). The '45' technique can also be extended to calculate cells from two or more connected rows, columns or (most commonly) nonets, in which case the solver has to refer to the multiples of 45 accordingly.

Initial analysis of the sample problem

Fewest possible combinations

The two cells in the top left must be 1+2. The 3 cells to the right totaling 15 cannot therefore have either a 1 or a 2, so they must be either 3+4+8, 3+5+7 or 4+5+6.

The two vertical cells in the top left of the top right nonet cannot be 2+2 as that would mean duplicates, so they must be 1+3. The 1 cannot be in the top line as that conflicts with our first 2 cells therefore the top cell of this pair is 3 and the lower cell 1. This also means the 3 cell cage 15 to the left cannot contain a 3 and so is 4+5+6.

Similarly the neighbouring 16 must be 9+7.

The four cells in the top right cannot include both 1 & 3, nor both of 9 & 7; If any of 1, 3, 7 or 9 are present then they must be the lone square in the nonet below. Therefore these 4 cells are one of 1+2+4+8, 1+2+5+7 or 2+3+4+6.

The 2 cells in the middle of the left edge must be either 1+5 or 2+4. And so on.

45

Looking at the nonet on the left hand side in the middle, we can see that there are three cages which do not cross over into another nonet; these add up to 33, meaning that the sum of the remaining two cells must be 12. This does not seem particularly useful, but consider that the cell in the bottom right of the nonet is part of a 3-cage of 6; it can therefore only contain 1, 2 or 3. If it contained 1 or 2, the other cell would have to contain 11 or 10 respectively; this is impossible. It must, therefore, contain 3, and the other cell 9.

Duplicate cell ambiguity

By convention in Japan, killer sudoku cages do not include duplicate numbers, even if they crossed nonets. When The Times first introduced the killer sudoku in 2005, however, the newspaper did not make this rule explicit. Even though the vast majority of sudoku puzzles followed the rule anyway, English-speaking solvers scratched their heads over appropriate solving strategies given the ambiguity. Within a month, though, the Times clarified the rule, and now the world standard is no duplicates within cages.

It is easiest to determine the combinations within large cages by means of complements. The table for 6 cell cages is the complement of the 3 cell table adding up to "45 - listed value"; similarly the 7 cell table complements the 2 cell table. An 8-cell cage is of course missing only one digit (45 - the sum of the cage).

External links

• Too good for Fiendish? Then try Killer Su Doku - article in The Times
• Killer Su Doku - some tips for solvers
• Killer Sudoku solving tips and example work through of a puzzle
• JC's Killer Sudoku - solving techniques
• DJApe's Killer Sudoku - solving tips
• SudoCue Killer solving guide
• Sudoku Tiger Killer Solving Guide

You Don't Have To Be Good

At Maths To Play Kakuro

You've probably entered a bookstore to see a table

overflowing with partially gridded numbers

pictured on the covers of numerous books titled 'Sudoku and Kakuro'

you believed you would have to be good at maths to play these games.

Kakuro is a great mental workout.

Keeps your mind sharp and mentally active.

It's great fun, addictive and inexpensive hobby.

Very much like Cryptic Crosswords Puzzles

Cross The only thing holding you back from

owning This magic game of logic is

THE SPEED OF YOUR IMPLEMENTATION