# Japanese Sums

## Rules

Place a digit from the specified list into some cells so that no digit appears more than once in each row or column. Cells may remain empty. Numbers outside the grid indicate all sums of continuous groups of digits (including "sums" of a single digit) along that row or column. These groups are separated by empty cells. These sums are given in the same order as their corresponding groups of digits.

(Rules and example from PGP IB)

## History of the puzzle

Contrary to its name, the puzzle was invented by Tim Peeters (Netherlands) in 2003. The name is an allusion to Paint by Numbers, known in Dutch as "Japanse puzzel" ("Japanese Puzzle"). First appeared on WPC 2003/Part V. This is one of the earliest Japanese Sums ever made.

According to Tim, the original idea came from the invention of Stef Keetman (Netherlands), a similar puzzle on a Hexagonal grid.

## Variants

### Japanese Sums and Products

Possibly German origin. One instance can be found in the 10th 24hPC[1] (2009). The author of the puzzle was either Roland or Ulrich Voigt.

Place a digit from the specified list into the grid, so that each number appears at most once in each row and column, and shade the remaining cells. The numbers outside the grid describe the contents of the respective row or column. Each number corresponds to a contiguous group of numbers (possibly a single number) and indicates either the sum or the product (or possibly both) of these numbers. Two such groups are separated by one or more shaded cells. For each row and column, the numbers outside are shown in the correct order.

(Rules (modified) and example (1-5) from WPC 2019 IB)

### Pentomino Japanese Sums

There are a few Japanese Sums variants involving pentominoes. The oldest one is probably this whopping 3D version by Peter Krah (Germany).

This one, a very natural hybrid, is the version that has appeared in WPC 2016/Round 17.

Place the given set of pentominoes into the grid. The pentominoes may be rotated and reflected, but they cannot touch each other, not even diagonally. Then fill in the blank cells with numbers from 1 to 9 so that, no digit is repeated within a row or column. The numbers outside the grid indicate the sums of consecutive blocks of numbers without black cells in between in the correct order. If there are more numbers outside the same row/column, there must be at least one black cell (part of the pentomino) between the blocks of numbers.

(Rules and example (3 Ns) from WPC 2016 IB)