# Kakuro

## Rules[edit]

Place a digit from 1 to 9 into each white cell. The numbers in grey cells indicate the sum of digits in the adjacent "word" across or down. (Across "words" are to the right of their sums, Down "words" are below their sums.) Digits may not repeat within a "word".

(Rules and example from PGP IB)

### Rule Variations[edit]

- Sometimes not all "words" have their provided sum provided.

## History of the puzzle[edit]

First appeared on one of the crossword magazines published by *Dell* magazines in 1950 under the name "Cross Sums." Invented by Jacob Funk (Canada).

The name カックロ ("Kakuro") was first given when the puzzle appeared on *Monthly Nikoli*. It is a contraction of 加算クロス ("Kasan Kurosu"), namely "Addition Cross(word)."

## Variants[edit]

### Multiplication Kakuro[edit]

Wikipedia article on Kakuro claims Dell published this as Product Cross but doesn't mention when they did so. ^{[1]} Probably in the 60's, at the height of the popularity in the Dell magazine's Sum Cross. Seen on WPC 1993, but its author is unknown.

Place a digit from 1 to 9 into each white cell. The numbers in grey cells indicate the **product** of digits in the adjacent "word" across or down. Digits may not repeat within a "word".

(Example from WPC 2018 IB)

### Domino Kakuro[edit]

First appeared on WPC 2003/Part VII, "Dominoes" round. Invented by Tim Peeters (Netherlands). ^{[2]}

Place the given domino set into the grid so that the sum in each consecutive rows and columns match their corresponding value. Numbers may not repeat in the same sum. Once all numbers are filled in, mark the locations of the dominoes. Each domino is used exactly once.

(Rules and example (0-1 to 2-3) from 24hPC 2014 IB)

### Math Kakuro[edit]

Can be seen in the 2006 Japan Semifinals under the name スケルマッス ("Skel(eton) Maths").^{[3]} The author of the puzzle is currently unknown. The name suggests it is intended to be a hybrid between Cross Maths and Crisscross (aka Skeleton). Cross Maths and this puzzle share the feature about operation precedence.

Fill in all empty white cells with numbers from 1 to 9 so that no digit is repeated within an equation. Numbers in grey cells are the results of these equations. There is no precedence of multiplication and division, the operations are always applied from left to right or from top to bottom.

(Rules and example from WPC 2016 IB)

### Gapped Kakuro[edit]

Invented by Serkan Yürekli (Turkey) for WPC 2010, but the puzzle he wrote wasn't used. The first appearance is the 11th 24-Hour Puzzle Championships (2010).^{[4]}

Place a digit from 1 to 9 in some of the empty cells. The sum of digits in each horizontal and vertical group of cells is given on its left and top respectively. Digits do not repeat within any set of consecutive empty cells. Some cells can be left blank but blank cells cannot touch each other by a side.

(Rules and example from WPC 2017 IB)

### Kropkuro[edit]

First appeared on Tawan Sunathvanichkul's (Thailand) contest held on Logic Masters India in 2011, *Puzzle Fusion*.^{[5]} Hybrid with Kropki.

Place a digit from 1 to 9 into each of the empty cells. The sum of digits in each horizontal and vertical group of cells is given on its left and top respectively. Digits do not repeat within any set of consecutive empty cells. If two consecutive digits appear in two neighbouring cells, they are separated by a white dot. If the digit in a cell is double the digit in the neighbouring cell, then they are marked by a black dot. The dot between 1 and 2 can either be white or be black.

(Rules and Example from *Puzzle Fusion* IB)

## Appearances in the past WPCs[edit]

- WPC 2019/Round 7 by Ulrich Voigt
- WPC 2019/Round 9 by Ulrich Voigt
- WPC 2019/World Cup Round 3 by Gabi Penn-Karras
- WPC 2019/World Cup Playoffs by Gabi Penn-Karras
- WPC 2018/Round 5 (Multiplication Kakuro) by Jan Zvěřina
- WPC 2018/Round 6 (Domino Kakuro) by František Luskač
- WPC 2018/Round 9 by Jiří Hrdina
- WPC 2017/Round 1 (Kropkuro) by Deb Mohanty
- WPC 2017/Round 9 (Gapped Kakuro) by Amit Sowani
- WPC 2016/Round 3 (Kropkuro) by Matúš Demiger
- WPC 2016/Round 8 (Math Kakuro) by Matúš Demiger
- WPC 2016/Round 13 (Irregular grid)
- WPC 2015/Round 9 ("with different areas")
- WPC 2015/Round 12 (Gapped Kakuro)
- WPC 2015/Round 14 (Coded)
- WPC 2014/Round 3
- WPC 2014/Round 10 (Nonconsecutive)
- WPC 2013/Part 2
- WPC 2013/Part 5
- WPC 2012/Part 2 (X Kakuro)
- WPC 2012/Part 3 (Hollow Kakuro)
- WPC 2012/Part 10 (Hexagonal)
- WPC 2011/Part 11 (Multiples Kakuro)
- WPC 2010/Part 2
- WPC 2010/Part 3 (Skykuro, Sudokuro)