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How to Play Kakuro Puzzles

Darius is a former high school literary and feature writer with a BS degree in Information and Communications Technology.

How to Play Kakuro Puzzles

How to Play Kakuro Puzzles

What Is Kakuro?

Kakuro is a logic and numbers game designed to test its players' abilities to think critically, logically, and mathematically. Often called Kakkuro or Kakoro, it is any puzzle game with a transliteration of crossword puzzles. The twist is that some of the rules follow that of Sudoku.

Solving the puzzles is similar to how crossword and Sudoku problems are solved; its rules almost intersect in the middle to give it its own identity. It has a lot of variations and a lot of methods for solving it. In fact, it is also the second most popular puzzle in Japan, next to Sudoku, and often played in World Puzzle Championship competitions.

But how do one solve Kakuro puzzles? And where did this puzzle, somehow, originated from? Read on to learn more about a very interesting logic and mathematics game that will surely and efficiently test your knowledge.


Rules of Kakuro

A kakuro puzzle is often 16x16 in dimensions, but these can also vary widely. They range from easy to hard difficulty, with shapes varying from squares, circles, hearts, to diamonds, trapezoids, and letters.

The small squares are often called cells, and a combination of adjacent horizontal and/or vertical squares are called blocks. There's also an unwritten yet always followed rule that the minimum number of cells per block should always be two and the maximum should be nine since one cell is either logically or mathematically impossible.

The total of a block must be equal to the sum of its corresponding "down" or "across," with the total summation already written in their cells. That means that if the puzzle has a horizontal block total of 6 (called a clue) with three missing cells, the answers to those cells could either be 1 + 2 + 3 or 3 + 2 + 1.

Of course, this depends because all of the answers affect the total summation of any affected total sum. For example, if any of the possible answers for "6" passes through or intersects any cell or block of another, like "8," either a 1, a 2, or a 3 will affect the vertical block total of 8 depending on your answer.

Blue goes from bottom to top, red goes from right to left. This applies to all the cells with total sums.

Blue goes from bottom to top, red goes from right to left. This applies to all the cells with total sums.

Like solving crosswords, each cell with a total should be answered by filling out the answers for the missing "down" and "across" blocks. The sum of each horizontal block equals the clue on its left (red), and the sum of each vertical block equals the clue on its top (blue).

And like solving Sudoku, only numbers 1 to 9 are used, and no same numbers should exist in any block at all times. The process often involves logical and mathematical combinations and permutations.

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Solving Kakuro puzzles also often involves using various logical and mathematical solving techniques, but sometimes winging it can be an option as long as the rule of non-duplication is followed. Advanced players would also memorize the possible numbers of the addition of each sum (45 being the maximum), along with their possible permutations and combinations.

The main objective of the game is to fill all the empty white cells with numbers from 1 to 9 without having any duplicates in its horizontal and vertical blocks, therefore answering all the clues. Imagine you're solving a crossword puzzle with a mix of Sudoku's rule where positive integers are placed instead of letters.

An example of a kakuro puzzle.

An example of a kakuro puzzle.

My Experience With Kakuro Puzzles

My first encounter with the game was during a high school math competition. We were given leaflets of paper with grids and boxes, and I initially thought we were going to solve some crossword puzzles. But when I looked at the paper, there were numbers printed on it along with ominous dashes on white boxes and blackened boxes. Our teacher then discussed the rules of the game. Creating and solving puzzles is one of my favorite pastimes, so I took on the challenge of solving my Kakuro puzzle. The fun of having a puzzle solved is both innately fun and satisfying.

A Brief History of Kakuro

Kakuro is a challenging and highly addictive math-and-logic puzzle game.

Kakuro is one of the oldest grid logic puzzles in existence, traced back to the April/May 1950 issue of Official Crossword Puzzles by Dell Publishing Company. They were intermittently published, rose to popularity during the 1960s, and were once called Cross Sums, which were regularly posted in the printed issues. The name Cross Sums (and Cross Additions) can be traced to a Canadian named Jacob E. Funk, an employee of Dell Magazines.

In 1980, Cross Sums were imported to Japan by Maki Kaji, president of Nikoli puzzles, who named them Kasan Kurosu—a combination of the Japanese word for "addition" and the Japanese pronunciation of the English word "cross." The name would then be rebranded into Kakuro after six years.

According to Maki Kaji, Kakuro was Nikoli’s top-ranking puzzle from 1986 to 1992. It was overtaken by Sudoku, which rules the top of the list until today.

Sparked by Sudoku’s sensational worldwide success, the Kakuro boom in the West started in September 2005 when The Guardian and The Daily Mail introduced daily Kakuro puzzles in the UK. Kakuro books were also exhibited at the Frankfurt book fair in 2005.

In 2006, Sterling Publishing released eight books with Conceptis Kakuro puzzles. Today, dedicated and mixed magazines and books with Kakuro by Conceptis are published regularly in 35 countries. Other variations of Kakuro would also take the spotlight, such as a cryptic Kakuro (where the numbers used are in cryptic puzzle form), reverse Kakuro (where the numbers are subtracted), and Cross Sums Sudoku (a Sudoku using Kakuro's rules).

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2020 Darius Razzle Paciente

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