Cop and Robber

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If playing outside, a tree, a playground set, or any large item outside can be considered the safe zone where the robbers cannot get caught and bean bags can be dropped off. If the bean bags are gone and all in the safe zone, the robbers win the game. If all of the robbers are sitting down, then that means they have all been arrested and the cops win the game.

There are kinds of skins provided. You can select your interested skin which makes you different with others. If the cop tags the robber that means he or she is caught them has been considered arrested by them and the robber has to sit down wherever they were tagged and remain in place if there is no bean bag in hand. It is best to always separate them according to these age groups. Six to nine years old should be one group of kids. Nine to twelve years old should be another set of kids. The game ends once all the robbers have been caught and sitting down. Sometimes the game goes a little longer than expected if there are faster robbers than cops, then the game can be timed since gym class only last an hour.

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On each subsequent turn, the player controlling the cops chooses a (possibly empty) subset of the cops, and moves each of these cops to adjacent vertices. The remaining cops (if any) stay put.

The point of the game is for the robbers to run around the gym and not get tagged by the cops who will be chasing them diligently.

Kids can get a little rowdy sometimes, so it is always best to remind them it has to be a tag only game. Like many sports are games everyone should stretch before doing such activities. The cop number of a graph G {\displaystyle G} is the minimum number k {\displaystyle k} such that k {\displaystyle k} cops can win the game on G {\displaystyle G} . [1] Example [ edit ]

If the robber runs to the hula hoop and has the bean bag in hand, as long as they stand inside to hula hoop they are considered safe and cannot be taken out the game. On a cycle graph of length more than three, the cop number is two. If there is only one cop, the robber can move to a position two steps away from the cop, and always maintain the same distance after each move of the robber. In this way, the robber can evade capture forever. However, if there are two cops, one can stay at one vertex and cause the robber and the other cop to play in the remaining path. If the other cop follows the tree strategy, the robber will eventually lose.By gradually moving closer together, two cops can eventually catch a robber on any cycle (here, a baseball diamond) The person leading the activity should begin the game by shouting ‘Go.’ The 'Cops' should spread out across the playing area and defend their area. The 'Robbers' should start from home base and try to avoid being tagged by the 'Cops'. Each item should be returned to home base. 'Robbers' who are tagged should also return to home base. Various game modes: Stronghold Mode & Team Death Match Mode & Killing Competition Mode & Peace Mode & Ghost Mode & Hide And Seek Mode & Arms Race. You can select your preferred mode to battle with a team or fight alone. Once either of these happens then the proper thing to do is have the cops and robbers switch places and play the game again. This allows each team to play both sides of the game. On the Playground or Anywhere Outside

is known. However, the problems of obtaining a tight bound, and of proving or disproving Meyniel's conjecture, remain unsolved. It is even unknown whether the soft Meyniel conjecture, that there exists a constant c < 1 {\displaystyle c<1} for which the cop number is always O ( n c ) {\displaystyle O(n Sometimes the player calls it quits once all the bean bags have been taken out of the hula hoops which would probably mean the bank goes bankrupt. Some of the fundamental skills that go along with cops and robbers is dodging, jumping, and running. Some of the other skills it takes to play this game is endurance and speed. In this game, one player controls the position of a given number of cops and the other player controls the position of a robber. The cops are trying to catch the robber by moving to the same position, while the robber is trying to remain uncaught. Thus, the players perform the following actions, taking turns with each other: [1]Henri Meyniel (also known for Meyniel graphs) conjectured in 1985 that every connected n {\displaystyle n} -vertex graph has cop number O ( n ) {\displaystyle O({\sqrt {n}})} . The Levi graphs (or incidence graphs) of finite projective planes have girth six and minimum degree Ω ( n ) {\displaystyle \Omega ({\sqrt {n}})} , so if true this bound would be the best possible. [3]