A carom or other board offers an ideally frictionless platform for the motion of objects (striker/coins), and controlling the motion of these objects to put them in the pockets is the challenge in the game. Existing kinds of this game rely on the player’s skill in choosing a set of coins to put in the pocket, relying on his/her skill in launching the striker with the correct velocity and direction to achieve this goal. In doing so, the primary challenge is to manage the collisions between the striker and/or coins and/or board sides to achieve a final velocity to a coin, putting it into the pocket. All forces in traditional carom are observed during contact of the striker and/or coins and/or board sides.
Magrom introduces non-contact magnetic forces into this game, by attaching magnets to the striker/coins/board. These magnets can be completely embedded in the striker/coins, so that the external appearance is exactly the same as conventional carom.
These forces cause the motion of the striker and/or coins to change direction, move together, etc without any visible collision or imposed external force. The resulting “swing areas (repulsive)” and “traps (attractive areas)” of the striker and/or coins make the game fascinating. Coins stick/repel to each other, at the locations where their magnetic poles lie. Proper strategies have to be devised to avoid putting coins in the vicinity of the swing and trap areas, where is it difficult to control them (unless a very high degree of mastery is achieved, where the magnetic field is used to advantage). Similar strategies have to be devised to handle the coins sticking to each other, and moving as a composite coin.
The amount of the non-contact magnetic forces can be customized, to achieve various levels of difficulty. Even at low levels of difficulty, the game is very entertaining, due to the swings, traps and coins sticking to/repelling each other.
There are many kinds of this game, some of which are shown below (see also the figures below).
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Magnetized striker and/or coins only: In this game, only one or more of the striker and/or the coins are magnetized in some fashion (possibly with multiple magnets – mono, dipoles, tripoles, …). All coins need not be magnetized, and the standard coins can be used in conjunction with magnetized coins. The coins attract/repel each other, while the board is neutral. Proper strategies have to be devised to, for example (a) separate different coloured coins, (b) moves coins of the same colour as a unit (c) move the queen and the current player’s coin as a unit, if they are stuck together, etc. An ordinary board can be used, only the striker and coins need to be different and purchased. Each coin can be magnetized in different ways, and a few kinds are shown in Figure 1 (a) (b) and (c). Note that the orientation of the magnetic field in each coin can be arbitrary – vertical, horizontal, or even at an angle. All magnets need not have the same orientation – see Figure 1 (d):
Figure 1 (a) Magnetized Striker and Coins – Monopole, Dipole and Tripole. Direction of magnetization is vertical (into/out of paper).
Figure 1 (b) Magnetized Striker and Coins –the magnet positions can be changed in a coin. Orientation of field is horizontal.
Figure 1 (c) General orientation of magnets relative to the striker/coins.
Figure 1 (d) Hybrid Magnetized Coins both with horizontal and vertical magnetization.
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Magnetized striker and/or magnetized coins and/or magnetized board:
Here the board is also magnetized in various ways, with magnets placed in various places beneath the surface. This causes potential wells to appear on the surface, and thereby modulate the behaviour of the coins, in an “invisible” manner. At places where the magnetic field attracts, the coins tend to get trapped, where it is repulsive they swing by, and so on. Traps on the sides prevent striker/coin rebounds.
Playing the game effectively requires reasonable skill to maneuver the coins away from these areas, or a very high degree of skill to exploit the magnetic fields in these areas. The skill is both in designing a proper route for the coins, and in striking the coins correctly to achieve the desired trajectory. Some kinds of this game are the 1, 2, 3 or 4 pouch kinds, where only 1, 2, 3 or all 4 pouches can be used for pocketing coins. Magnets near/in disallowed pouches prevent coins from being pocketed there.
In one version, there are a variety of strikers, and depending on the board state, the player can select the one to use in the next strike (for a low level version), or the opponent can choose the striker depending on the state of the board.
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The magnetization of the coins causes them to attract/repel each other. The coins will tend to occupy relative position such that the magnets of one attract the magnets of another. As such, the system of coins displays stable states (energy minima), which can be used to illustrate many concepts.
Figure SEQ Figure \* ARABIC 2: Illustrating different stable geometrical structures built from magnetic coins (a) Linear chain of 4 (b) Tree of 3 (c) DAG of 5
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The attraction between coins offers the possibility of them forming interesting geometrical shapes – a tree, a dag, etc. The entire game can be played with all or part of the coins forming this shape, and moved together as a unit. Conceptually, the individual coin is an atom, and the entire shape is a molecule. The number of combinations is very large, corresponding to graph combinatorics.
More points can be allocated towards moving the whole coin as a unit, till at least one of them is in or over the pocket. Then we can get points for all the coins (subject to a possible limit). The number of possible geometrical shapes is combinatorial, and counting these is itself very interesting to children.
Children can be asked to make different kinds of geometrical patterns, and move them as a unit without rotation (say). Moving a whole coin without rotation as a unit teaches them concepts of center of mass, etc. The striker has to hit the pattern near the center of mass, else the pattern will rotate. Children should explain in which case it is possible to move the pattern without rotation, and in which case it is not possible (this depends on the orientation of the pattern w.r.t the side the child/player is in).
If they are unable to move the pattern as a unit, then they can break them up, for a penalty. There are many strategies to play such games, and the rules of one possible such game are described later.
Instead of putting in a pocket, coins can be arranged at one side, and the objective is to make a certain pattern of attached coins using the striker. One player plays till the pattern is made, or a maximum number of strikes is exhausted. Then the other player plays. The player who takes fewer strikes wins.
Figure SEQ Figure \* ARABIC 3: Illustrating data storage concepts using relative location of coins (a) representing (0) and (b) representing (1)
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Considering data storage, two coins A and B, with the north of A sticking to the south of B, can represent a 0, and vice versa for a 1. As such, an interesting game can be just arranging the coins such that particular stable states (“data messages”) are formed.
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In all the above, electromagnets can be used on striker/board/coins, in addition to / instead of permanent magnets. The magnetic fields can then be changed by the players during the play itself. In one embodiment, the opponent can change the magnetic field to challenge the player.
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The magnetic field can be changed dynamically also during play.
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In all the above, we can use induction members and/or hysteresis members, which offer “drag”, which can slow down striker/coins, offering more variety in the game.
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Instead of and in addition to magnets, we can use physical obstacles (say wooden obstacles) placed on the board, which will act like hard barriers. These barriers do not act at a distance (neither attract nor repel), but collide elastically (or inelastically, depending on the material). The game then is played to go around these obstacles.
Figure 1 (a) Magnetized Striker and Coins – Monopole, Dipole and Tripole. Direction of magnetization is vertical (into/out of paper).
Figure 1 (b) Magnetized Striker and Coins –the magnet positions can be changed in a coin. Orientation of field is horizontal.
Figure 1 (c) General orientation of magnets relative to the striker/coins.
Figure 1 (d) Hybrid Magnetized Coins both with horizontal and vertical magnetization.
Here the board is also magnetized in various ways, with magnets placed in various places beneath the surface. This causes potential wells to appear on the surface, and thereby modulate the behaviour of the coins, in an “invisible” manner. At places where the magnetic field attracts, the coins tend to get trapped, where it is repulsive they swing by, and so on. Traps on the sides prevent striker/coin rebounds.
Playing the game effectively requires reasonable skill to maneuver the coins away from these areas, or a very high degree of skill to exploit the magnetic fields in these areas. The skill is both in designing a proper route for the coins, and in striking the coins correctly to achieve the desired trajectory. Some kinds of this game are the 1, 2, 3 or 4 pouch kinds, where only 1, 2, 3 or all 4 pouches can be used for pocketing coins. Magnets near/in disallowed pouches prevent coins from being pocketed there.
In one version, there are a variety of strikers, and depending on the board state, the player can select the one to use in the next strike (for a low level version), or the opponent can choose the striker depending on the state of the board.
Figure SEQ Figure \* ARABIC 2: Illustrating different stable geometrical structures built from magnetic coins (a) Linear chain of 4 (b) Tree of 3 (c) DAG of 5
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The attraction between coins offers the possibility of them forming interesting geometrical shapes – a tree, a dag, etc. The entire game can be played with all or part of the coins forming this shape, and moved together as a unit. Conceptually, the individual coin is an atom, and the entire shape is a molecule. The number of combinations is very large, corresponding to graph combinatorics.
More points can be allocated towards moving the whole coin as a unit, till at least one of them is in or over the pocket. Then we can get points for all the coins (subject to a possible limit). The number of possible geometrical shapes is combinatorial, and counting these is itself very interesting to children.
Children can be asked to make different kinds of geometrical patterns, and move them as a unit without rotation (say). Moving a whole coin without rotation as a unit teaches them concepts of center of mass, etc. The striker has to hit the pattern near the center of mass, else the pattern will rotate. Children should explain in which case it is possible to move the pattern without rotation, and in which case it is not possible (this depends on the orientation of the pattern w.r.t the side the child/player is in).
If they are unable to move the pattern as a unit, then they can break them up, for a penalty. There are many strategies to play such games, and the rules of one possible such game are described later.
Instead of putting in a pocket, coins can be arranged at one side, and the objective is to make a certain pattern of attached coins using the striker. One player plays till the pattern is made, or a maximum number of strikes is exhausted. Then the other player plays. The player who takes fewer strikes wins.
Figure SEQ Figure \* ARABIC 3: Illustrating data storage concepts using relative location of coins (a) representing (0) and (b) representing (1)
- Considering data storage, two coins A and B, with the north of A sticking to the south of B, can represent a 0, and vice versa for a 1. As such, an interesting game can be just arranging the coins such that particular stable states (“data messages”) are formed.