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Mū Tōrere is a traditional Māori blocking game from New Zealand.

The game was first described in print by Best (1917), and this description is based upon his.

It is said that the Ngāti Haua chief Wiremu Tamihana Te Waharoa once offered to play Mū Tōrere with Governor Grey, with the whole country as a stake — Grey apparently declined.B[p. 54]



A married couple (Te Urikore at left and Te Rangiua at right) playing Mū Tōrere, c. 1910.

© , used with permission: PAColl-5671-07

The board used in the game has a central spot (putahi ‘centre’) as well as eight arms or ‘tentacles’ (kāwai) arranged around the central spot. In this way, the board resembles an octopus, and modern commercial versions of the game are often octopus-themed.

Each player has four pieces in a different colour from their opponent, which begin the game placed in a single cluster at the end of four of the eight arms.

On each player’s turn they must move one piece either from one arm to an adjacent arm which does not have a piece on it, from an arm to the central spot if it is empty, or from the central spot to any empty arm. The goal is to block the other player so that they are unable to move; if this is done, the blocking player wins.

To start the game, the first player must move one of the two pieces at the end of their cluster, as moving one of the central two pieces would result in an instant victory.


For analysis, see Ascher (1987); Straffin (1995); Straffin (1996). With perfect play, the game is a draw.

See also

Some general references are: The Oxford History of Board Games, Math Games & Activities from Around the World (p. 34).


  1. (). ‘⁨⁩’. Man vol. 17, : pages 14–15.

  2. and (). ⁨Taonga Tuku Iho: Illustrated Encyclopedia of Traditional Māori Life⁩. New Holland⁩: London, England, UK. ISBN: 978-1-877246-90-6.

  3. (). ‘⁨⁩’. Mathematics Magazine vol. 60 (2), : pages 90–100.

  4. (). ‘⁨⁩’. Mathematics Magazine vol. 68 (5), : pages 382–386.

  5. (). ‘⁨⁩’. Mathematics Magazine vol. 69 (1), : page 65.

  6. (). ⁨⁩. Oxford University Press⁩: Oxford, England, UK. ISBN: 978-0-19-212998-7.

  7. (). ⁨Math Games & Activities from Around the World⁩. Chicago Review Press⁩: Chicago, IL, USA. ISBN: 1-55652-287-8.


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