# Antimagic Square

## Rules[edit]

Place numbers from 1 to 2N into all the cells so that there are exactly two numbers in each row, column and main diagonal. (N is the number of cells in a row.) For all combinations of two numbers in each row, column and diagonal, each of their sums are different, varying in some consecutive range. Some of the sums are shown around the grid.

(Rules (modified) and example (N=4, 3 to 15) from WPC 2018 IB)

## History of the puzzle[edit]

The "Antimagic Square", which is more similar to the original magic squares, was defined by J.A. Lindon in 1962. ^{[1]} All cells were filled with numbers from 1 to N^2.

This ruleset probably first appeared on WPC 2001/Part 2. The puzzle was written by František Luskač (Czech Rep).

## Variants[edit]

### Antimagic Hexagon with Double Cells[edit]

Appeared on WPC 2018/Round 4. Puzzle was written by František Luskač (Czech Rep).

Place numbers from 1 to N into some of the cells. For rows marked with an arrow, sum of their contents are different, varying in some consecutive range. Some of the sums are shown around the grid.

(Example (N=6, 3-11) from WPC 2018 IB)

## Appearances in the past WPCs[edit]

- WPC 2018/Round 4 (Hexagonal with Double Cells) by František Luskač
- WPC 2018/Round 9 by František Luskač