# Numbered Regions

## Rules[edit]

Assign one number from 1 to X to each region so that each number is used exactly once. The numbers in the shaded cells indicate the sum of the numbers in regions sharing at least one side with this cell. (each region is counted just once in the sum)

(Rules and example (X=6) from WPC 2018 IB)

### Rule Variations[edit]

- From WPC 2019: Each region has a clue which indicate the sum of the entered numbers of the region itself and all adjacent regions. Regions are considered adjacent if they are sharing an edge.

## History of the puzzle[edit]

This article is named after a WPC 2018 puzzle, but similar puzzles have independently been published multiple times. Mathematically, this puzzle is just a set of Diophantine equations.

For example, the following is the rules of a puzzle called "Value Added" from WPC 1996: "Each of the rectangles has a value between 1 to 9. Each value occurs only once. When two or more rectangles overlap, their values are added. We have indicated some of these sums in the diagram. What are the values of rectangles A to I?"

## Variants[edit]

### Star[edit]

Rules: Place all the numbers from a given range in the empty cells so that the sum of the numbers on the vertices in all five quadrangles is N. The sum of numbers on the circle is M higher than the sum of numbers on the ouside.

(Example (1-10, N=18, M=-22) from WPC 2018 IB)

This name was given to a puzzle in WPC 2018/Round 9. Essentially the same as Numbered Region, plus the rule on inside-outside difference.

Similar puzzle was present in a 2012 Czech competition ("Prostějov GP"). The puzzle was written by František Luskač under the name **Čokoláda Orion** ("Chocolate Orion", a Czech chocolate brand, whose logo is star-shaped).

## Appearances in the past WPCs[edit]

- WPC 2019/Round 11 by Ulrich Voigt
- WPC 2018/Round 9 by Jiří Hrdina
- WPC 2018/Round 9 (Star) by František Luskač
- WPC 2017/Round 16 by Amit Sowani