The first game of the 2013 World Chess Championship, Carlsen vs. Anand, ended in a draw after just 16 moves.
Is this shortest game in the history of the World Chess Championship?
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There have been some shorter ones, for instance
Kasparov-Kramnik (2000), game 7, draw in 11 moves.
Kasparov-Anand (1995), game 18, draw in 12 moves.
Karpov-Kasparov (1984), game 29, draw in 13 moves.
The shortest games in WCC history I believe are the two 10 move draws at the end of the 1963 Botvinnik-Petrosian match, but it's clear Botvinnik had more or less given up the match before those games.
The shortest decisive game in a WCC match is reportedly Anand-Gelfand (2012), game 8, in which black resigned before his 17th move:
Technically speaking, the shortest game in a World Championship is Game 2 of the Fischer vs Spassky Match 1972, where Fischer did not show up to play and lost by forfeit. Fischer was supposed to play White in this game, so no moves were made on the board.
Another similar situation occured in Game 5 of Topalov vs Kramnik World Championship match in 2006, where Kramnik who was supposed to play White didn't show up for the game.