Magnets

Rules

The grid is partitioned into regions of two square cells each (note that only region borders are drawn). Put "positive" (+) and "negative" (–) symbols into some cells, at most one symbol per cell, such that each region either has two symbols or no symbols at all. Adjacent cells (even within a region) cannot contain the same symbol.

The numbers above and to the left of the grid indicate the exact number of symbols of the specified type that must be placed in each column or row, respectively. If a number is not given, there might be any number of symbols of the specified type.

(Rules and example from PGP IB)

History of the puzzle

Invented by Jaroslav Müller (Czech Rep.). First appeared on WPC 2001/Part 13. The round consisted of 6 Magnets puzzles.

Variants

Anti Magnets

Invented by Silke Berendes (Germany) in 2010. First appeared on Logic Masters 2010 Qualifier.

Fill the grid with neutral (shaded) and magnetic plates. Each magnetic plate has two poles, represented by + and − signs. Poles of different types that are part of different plates cannot be horizontally or vertically adjacent. The numbers indicate how many poles of the corresponding type appear in the respective row or column.

(Rules and example from WPC 2019 IB)

Coral Magnets

First appeared on WPC 2015/Round 5. The puzzle was by Andrey Bogdanov (Russia). Additional restriction on shaded cells is based on Coral.

Apply normal Magnets rules.

Additionally, Shaded cells should form an area which is connected horizontally or vertically and contains no 2x2 shaded areas. The area can’t touch itself, not even diagonally.

(Additional rules and example from WPC 2015 IB)

Twilight Magnets

First appeared on WPC 2019/Round 8, a "Twilight" round. The puzzle was by Rainer Biegler (Germany).

Apply normal Magnets rules.

Additionally, plates with given symbols can either be shaded or keep their poles. Their polarity cannot be reversed.

(Additional rules and example from WPC 2019 IB)