to 32 spots. They have extended the computation up to 44 spots in 2011, and three isolated starting positions, with 46, 47 and 53 spots. The normal-play results so far are all consistent with the conjecture of Applegate, Jacobson, and Sleator. Misère version The computation history of the misère version of Sprouts is very similar to that of the normal version, with the same people involved. However, the misère version is more difficult to compute, and progress has been significantly slower. In 1990, Applegate, Jacobson and Sleator reached up to nine spots. Based on their results, they conjectured that the outcome follows a regular pattern of period five. However, this conjecture was invalidated in 2007 when Josh Jordan and Roman Khorkov extended the misère analysis up to 12 spots: the 12-spot misère game is a win, and not the conjectured loss. The same team reached up to 16 spots in 2009. The same year, Julien Lemoine and Simon Viennot reached 17 spots with complicated algorithms. They were able to extend their analysis up to 20 points in 2011. The results for misère play are now conjectured to follow a pattern of length six (with some exceptional values): the first player wins in misère Sprouts when the remainder (mod 6) is zero, four, or five, except that the first player wins the one-spot game and loses the four-spot game. The table below shows the pattern, with the two irregular values in bold. Brussels Sprouts A variant of the game, named Brussels Sprouts after the cruciferous vegetable, starts with a number of crosses, i.e. spots with four free ends. Each move involves joining two free ends with a curve, again not crossing any existing line, and then putting a short stroke across the line to create two new free ends. This game is finite, and the total number of moves (and thus the game's winner) is predetermined by the initial number of crosses: the players cannot affect the result by their play. Each move removes two free ends and introduces two more. With n initial crosses, the number of moves will be 5n − 2, so a game starting with an odd number of crosses will be a first player win, while a game starting with an even number will be a second player win regardless of the moves. To prove this (assuming that the game ends), let m denote the number