# Equal Sums

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## Rules[edit]

Insert one number from 1 to N (where N is the number of circles) into each circle, so that the sum of numbers on each line or curved line is the same. Every number must be used exactly once. The sum will be given in a circle next to the figure.

(Rules and example from WPC 2016 IB)

## History of the puzzle[edit]

This puzzle is a direct generalisation of magic squares. Magic squares were known to ancient Chinese mathematicians at least since 1st century BCE. ^{[1]} Since then, many generalisations of magic squares were considered. Some hexagonal examples of those are listed in Jürgen Köller's website. ^{[2]}

See also Numbered Regions.

## Appearances in the past WPCs[edit]

- WPC 2016/Round 2 by Matej Uher