Sim or Shim is a Korean surname. There are six Shim clans in Korea based in the regions ofCheongsong, Pungsan, Samcheok, Buyu, Uiryeong, and Jeonju. The biggest Sim clan is Cheongsong; they comprise about 85% of the all those with the surname Shim. Fourteen percent of all Korean Shims are members of the Pungsan and Samcheok clans. As of 2000, there were 252,255 people with this surname in South Korea, less than 1% of the population.
Sim is the third album by Brazilian singer-songwriter Vanessa da Mata, released on May 28, 2007 by Sony BMG. It was partially recorded at Kingston, Jamaica with musicians Sly & Robbie. It spawned the hit single "Boa Sorte/Good Luck", a duet with Ben Harper, which peaked at number one in both Brazil and Portugal, and was the most played song in Brazilian radio stations in the year of 2008. The second single, "Amado", also became a number-one hit in Brazil and the 15th most played song in the same year.
The game of Sim is played by two players on a board consisting of six dots ('vertices'). Each dot is connected to every other dot by a line ('edge').
Two players take turns coloring any uncolored lines. One player colors in one color, and the other colors in another color, with each player trying to avoid the creation of a triangle made solely of their color (only triangles with the dots as corners count; intersections of lines are not relevant); the player who completes such a triangle loses immediately.
Ramsey theory can also be used to show that no game of Sim can end in a tie. Specifically, since the Ramsey number R(3,3)=6, any two-coloring of the complete graph on 6 vertices (K6) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K6. For another proof that there must eventually be a triangle of either color, see the Theorem on friends and strangers.
Computer search has verified that the second player can win Sim with perfect play, but finding a perfect strategy that humans can easily memorize is an open problem.