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Sim (pencil game)

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 (K) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K. 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.

A self-improving Java applet including its source code is available for online play against a computer program.

The game of Sim is one example of a Ramsey game. Other Ramsey games are possible. For instance, the players can be allowed to color more than one line during their turns. This game also can be played with the Java applet mentioned above.

Another Ramsey game similar to Sim and related to Ramsey numberR(4,4)=18, which again cannot end in a tie, is played on 18 vertices and the 153 edges between them. The two players must avoid to color a monochromatic tetrahedron (a three-dimensional pyramid with four triangular faces).

The Ramsey numberR(3,3,3)=17 implies that any three-coloring of the complete graph on 17 vertices must contain a monochromatic triangle. A corresponding Ramsey game uses pencils of three colors. One approach can have three players compete, while another would allow two players to alternately select any of the three colors to paint an edge of the graph, until a player loses by completing a monochromatic triangle. Finding perfect winning strategies for these variants is most likely out of reach.

A technical report by Wolfgang Slany is available online, with many references to literature on Sim, going back to the game's introduction by Gustavus Simmons in 1969, including proofs and estimates of the difficulty as well as computational complexity of Sim and other Ramsey games.

Sim

Sim or SIM may refer to:

Sim (Korean surname)

Sim or Shim is a Korean surname. There are six Shim clans in Korea based in the regions of Cheongsong, 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 (album)

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.

Sim (actor)

Sim (July 21, 1926, Cauterets, Hautes-Pyrénées — September 6, 2009) was a French humorist, writer and comedian.

Born as Simon Jacques Eugène Berryer, he was part of the team of Les Grosses Têtes, a humoristic program on radio and TV. He also played the part of Geriatrix in Asterix movies ( Asterix and Obelix vs Caesar and Astérix at the Olympic Games).

Sim (surname)

As a surname, Sim may refer to

  • the Korean family Sim
  • the Chinese family Shen
  • Sim (Scottish surname)

SIM (film)

SIM is a 2013 Malayalam film directed by Diphan, featuring Ann Augustine, Deepak, Manikandan in lead roles. SIM, which is an acronym for "Sorry I am Mad", was produced by Royson Vellara. The film released on 19 March 2013.

SiM (band)

SiM is a Japanese alternative metal band from the Kanagawa Prefecture formed in 2004.

Wiktionary

sim

n. (context informal English) A simulation.

Usage examples of "sim".

Cholecystotomy for the relief of the distention of the gallbladder from obstruction of the common or cystic duct and for the removal of gall-stones was first performed in 1867 by Bobbs of Indianapolis, but it is to Marion Sims, in 1878, that perfection of the operation is due.

Early next day, Monday, the young dalesman set about inquiries among the townspeople as to whether a man answering to the description which he gave of Sim had been seen to pass through the town.

Ela fez que sim e olhou sorrindo para a mulher dele e, depois, para os filhos.

If these were the sims from the globulin farm, what were they doing here?

Sim slowed more, and Keri kept shoving his shield too far to one side.

Chion, Sim, and Lyte, together, followed by the others, all children growing swiftly into fighting men.

Pushing Lyte abruptly aside he seized upon a rock and dealt Sim a jolting blow upon his ankle that laid wide the flesh.

Sim leaped up, caught at an overhanging rock, locked Lyte in his legs, and drew himself hand over hand upward.

Elizabeth aslumber, but the sims also awake, and at frolic meseems, from the noises up the stairway.

Sim was enjoying himself debating through the menu with two white-jacketed waiters in voices raised over the hubbub of diners noshing and talking.

I dropped in to see Forrest, and Rosario and a friend of hers snuck aboard my plane and started running dry sims in the cockpit.

Domine, ab vitiis meis, ut solius tuae voluntatis mihi cupidus sim, et vocationis .

It had been fun meeting Roxanne Roc and playing with Sim Chick, and Tweeter had taught Sim some dirty bird jokes that no nonbird would understand.

And finally, I moved out of the Sim Room altogether, and set up my personal traveling zendo in the second of the two good spots I had mentally marked on the Upper Ag Deck.

In a few minutes the three men had drawn up at the cottage on the breast of Brandreth where Sim had asked for a drink.