Japanese Sums

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Japanese Sums Example.png Japanese Sums Example Solution.png

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[edit]

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


Japanese Sums and Products[edit]

Japanese Sums and Products Example.png Japanese Sums and Products Example Solution.png

Possibly German origin. One instance can be found in 24hPC 2009. 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 correct order.

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

Appearances in the past WPCs[edit]