Magic square

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Magic square
Type: brain game, Group dynamics game
Number of players: 8, 15 or 24
Location: small playing field
Equipment: a sheet of paper in A4 format
Duration: 15 to 20 minutes
Preparation: labelling sheets of paper

The Magic square (also: 15 puzzle) is a game of cooperation for groups and is equivalent to the eponymous brain game. It is more suitable for adolescents than children. It can only be played with a certain number of people: 8, 15 or 24 players.


One sheet of paper (about letter size) per player with the player's name written on it.


The sheets are labelled with the names of the participants, shuffled and arranged in a square (3x3, 4x4, 5x5). The inscription on the sheet should face the floor, thus, should not be readable. An additional (empty) sheet completes the square.


The players position themselves on the sheets in random order. One sheet is not occupied. Then the sheets are turned over in order to reveal the names.

Subsequently, the participants have to solve the Magic square: In the end, every player has to stand on the sheet carrying their name. In order to achieve that, one is only allowed to move vertically or horizontally from one sheet to the neighboring one, provided this sheet is the one not occupied by any other player.

Here is a simple approach to the solution (the full stop is the non-occupied sheet; the initial situation is on the left, the final situation on the right).

1.3    123    123    123 
426 => 4.6 => 456 => 456
758    758    7.8    78.

First, player 2 switches to the upper position, then player 5 switches to the upper position, and then player 8 switches to the position on his left. The final situation has been achieved, given that all players are standing on the sheet labelled with their name.

An additional obstacle is that at the beginning no participant knows their final position. Hence, the empty sheet is unveiled and announced in the first rounds. By doing this, all final positions are revealed bit by bit.