FIELD OF THE INVENTION

The present invention relates to a variant carom game wherein strikers and carom-men or coins are made of different materials, magnetized and non-magnetized along with set of 'fun-rules' to teach the kids about basics of physics and mathematics like Newton's Law, electromagnetism etc. The magnetic fields involved are safe, with strengths as per international safety limits.

BACKGROUND

We enhance the game of carom with magnets on the striker and/or the coins and/or the board. The resulting magnetic carom introduces a new dimension to the game - invisible magnetic forces by attaching magnets to the striker/coins/board. The coins get "trapped" in attractive wells, "swing" by repulsive areas, and stick/repel each other. All this makes the game interesting and challenging to play.

Many games can be created with a specified set of predefined rules for each.. The game can be played either single player or multi-player. A robotic player can be made for people to play against, and test and/or improve their skills. A completely software implementation can also be made.

In a specific embodiment, rare-earth magnets are used. This embodiment is cost effective, since modern rare-earth magnets are inexpensive. The game is also very educative, especially in fundamental physics (Newton's laws and electromagnetism). As such this is a simple entertaining and educative toy.

PRIOR ART DISCUSSION

The prior art (US Patent 7348754, 7733050) discussed the use of electromagnetic force/torque, using possibly induction and/or hysteresis, for control of motion in unpowered apparatus and in apparatus driven by electric motors or other prime movers. One objective of certain embodiments of the prior art invention is to extend the domain of electric motor speed control (and general motion control-possibly unpowered or utilizing other prime movers), traditionally characterized by electronic techniques, to small apparatus, like bubble vibration toys, paper dispensers, well pulleys, toothbrushes, display turntables, rotating lollipops, (very-low-cost) timing cams, toy racing cars, drawers, hinged objects, board games, etc.

The prior art stated above documents some features of this game and this document expands on the same with new material.

SUMMARY OF THE INVENTION

A carom or other board offers an ideally frictionless platform for the motion of objects (strikers/coins), and controlling the motion of these objects to put them in pockets is the challenge in the game. Existing variants 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 (a) select a set of coins to pocket and (b) 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 the forces in traditional carom are observed during contact of the striker and/or coins and/or board sides.

Our variant introduces magnetic forces, (which can act without contact) into this game, by attaching magnets to the striker and/or coins and/or board. These magnets can be completely embedded in the striker and/or coins and/or board, 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, multiple coins to move together as a unit, coins to repel each other, etc without any visible collision or imposed external force. The resulting "swing areas (repulsive)" and "traps (attractive areas)" of the striker and/or coins and/or board make the game fascinating. Coins stick to and/or repel 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, and moving as a unit.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 illustrates study of Newton 1st and 3rd laws of motion through a game of carom.

Figure 2 illustrates study of Newton's 2nd Law (F=ma) through a game of carom.

Figure 3 illustrates study of collision through a game of carom.

Figure 4 illustrates study of oscillations through a game of carom.

Figure 5(a) illustrates magnetized striker and coins with monopole, dipole and tripole wherein the direction of magnetization is vertical (into/out of paper). Only the pole on the top is visible, the other is below.

Figure 5(b) illustrates magnetized striker and coins with the magnet positions and/or orientation changeable in a coin wherein the orientation of the field is horizontal.

Figure 5(c) illustrates general orientation of magnets relative to the striker/coins.

Figure 5(d) illustrates hybrid magnetized coins both with horizontal and vertical magnetization.

Figure 6 illustrates different stable geometrical structures built from magnetic coins such as linear chain of 4 coins; tree of 3 coins and DAG of 5 coins.

Figure 7 illustrates data storage concepts using relative location of coins representing (0) and (1).

Figure 8 illustrates field distribution of exemplary coin.

Figure 9 illustrates web cam enabled quantitative carom showing conservation of linear and/or angular momentum.

Figure 10 illustrates a striker with a magnetic dipole, with eddy current forces enhanced due to closure of current loops.

Figure 11 illustrates various kinds of game dynamics

Figure 12(a) and (b) illustrates additional game dynamics where a tree is formed from a linear chain and a lone coin..

Figure 13(a) and 13(b) illustrates more game dynamics, where the tree is further modified to make a dag.

Figure 14(a) illustrates a picture of carom coin with 2 magnets.

Figure 14(b) illustrates a picture of carom coin with 4 magnets.

Figure 14(c) illustrates a picture of carom coin with 6 magnets.

Figure 15(a) illustrates a possible situation of pocketing two coins.

Figure 15(b) illustrates a situation where 2 coins are not pocketed.

Figure 15(c) illustrates a situation where 3 coins are pocketed.

Figure 15(d) illustrates a situation where 3 coins are not pocketed.

Figure 16 (a) through (i) shows the initial setup for several game variations.

Figure 17 shows an embodiment of a magnetic snooker game.

Figure 18 (a) shows the picture of an automatic carom player.

Figure 19 shows the picture of a magnetic coin with 6 dipolar magnets and tape covering them.

DETAILED DESCRIPTION OF PREFERED EMBODIMENTS

In our numbering scheme, unless otherwise specified, numbers of a part of a type "A", do not conflict with numbers of another part of a type "B", whether in the same figure or not Also, part numbers in different figures do not conflict Hence "magnet 100", and "coin 100" are different entities, whether in the same figure or not Also, "coin 100" in Figure 1 (a) and "coin 100" in Figure 1 (b) are different parts by default, and different from "coin 100" in Figure 2.

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 variants 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 (a) select a set of coins to pocket and (b) 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.

Our variant introduces magnetic forces into this game, by attaching magnets to the striker/coins/board. These magnets can be completely embedded in the striker and/or coins and/or board, so that the external appearance is exactly the same as conventional carom.

Our variant of carom has strikers and carom-men (referred to as a "coin" below) made of different materials, magnetized and non magnetized along with set of rules to create a variety of entertaining and educative games.

The magnetic 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 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.

A few of the concepts, which can be illustrated while having fun, are listed below:

1. Figure 1 illustrates two of Newton's laws - the law of inertia and the law of equal action and reaction. Given the ability to measure velocities (using exemplarily a camera mounted over the board), it can be verified that the velocity of the blue coin does not change, since there is no force acting on it after it is launched (inertia). Similarly, it can be verified that the velocities of two identical red coins coming towards each other before and after impact are the same, but reverse sign (action = reaction). Note that we do not need to launch both coins towards each other, it suffices to launch one, since all velocities can then referred to the center of mass frame (which is at the midpoint of the two red coins).

2. Figure 2 illustrates Newton's 2nd Law - F=ma (force = mass x acceleration). Using, exemplarily a spring of known spring constant K, and measured compression distance, a known force can be applied to a coin/striker, and the velocity as a function of time measured using a camera, and F=ma verified. There are other methods of applying such controlled forces also.

3. Figure 3 illustrates collision principles wherein the conservation of momentum, and the motion of the center of mass can be illustrated by having two coins/strikers collide, and measuring all velocities (vector velocities), etc as a function of time.

4. Figure 4 illustrates the principle of a simple oscillator. A stationary magnet kept beneath the board, attracts a coin on top which is also magnetized. The coin is given a push, and then it starts oscillating around the magnet kept beneath the board. From the masses of the coin, and the period of oscillation, the effective spring constant etc can be inferred. The harmonic nature of the oscillation can also be inferred by checking if the velocity profile of the coin is sinusoidal. The nonlinear nature of the magnetic forces w.r.t separation can be examined by comparing the periods for small/large amplitude oscillations.

Magnetic attraction/repulsion, eddy currents, hysteresis, etc can also be illustrated by this game. Eddy currents and hysteresis effects introduce controllable drag, and can be used to demonstrate concepts of friction quantitatively. Some details are given later.

MAGNETIC CAROM INFRASTRUCTURES:

All these concepts and more can be learned while a variety of games, with different infrastructures, are played. Some of the many possible infrastructures possible in magnetic carom are explained below: 1. 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 etc). 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 color 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. Each coin can be magnetized in different ways, and a few variants are shown in Figure 5 (a) (b) and (c). In Figure 5(a), Coin 100 has only one magnet- magnet 100, which has the South Pole facing upwards (north pole facing downwards contacting the board surface). Coin 200 has two magnets, magnets 100 and 200. Magnet 100 has South Pole facing upwards and the North Pole below. Magnet 200 has North Pole facing upwards and South Pole facing below. Coin 300 has three magnets, magnet 100 (south pole facing up), magnet 200 (north pole facing up), and magnet 300 (south pole facing up).

In Figure 5(b), Coin 100 has magnets in a horizontal orientation (north pole of magnet 200, is facing the side of the coin, pointing outwards). The positions of magnet 100, magnet 200, magnet 300 and magnet 400 can be changed. The coin 200 has 3 magnets, magnet 100, magnet 200 and magnet 300 in horizontal orientation. Coin 300, compared to coin 200, illustrates that the magnet positions are changeable, for magnets 100, 200 and 300. Coin 400 has magnets 100 and 200 situated in diametrically opposite ends and magnets 200 and 400 situated at diametrically opposite ends. All four magnets are situated at equal spreads around the coin 400. Magnets 100 and 400 have north pole facing outwards. Coin 200 and 300 have the south pole facing outwards.

In Figure 5(c), in coin 100, magnet 100 is situated at an angle. The vertical axis of the magnet makes an acute angle with respect to the vertical axis of the coin.
Note that the orientation of the magnetic field in each coin can be arbitrary - vertical, horizontal, or even at an angle (Figure 5 (c)). All magnets need not have the same orientation - see Figure 5 (d). In figure 5(d), the coins are hybrid, with varying orientation of magnets in them. In coin 100, magnets 200, 300 and 400 have horizontal orientation, while magnet 500 has vertical orientation. In coin 200, magnet 200, 100 and 300 have horizontal orientation and magnet 400 has vertical orientation. In coin 300, magnets 100, 200 and 300 have horizontal orientation and magnet 400 has vertical orientation. In coin 400, magnets 100, 200, 300 and 400 have horizontal orientation, and magnet 500 has vertical orientation.

2. 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/hills to appear on the surface, and thereby modulate the behavior of the coins, in an "invisible" manner. At places where the magnetic field attracts, the coins/striker 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 (a) select coins to pocket and (b) maneuver the coins away from trap 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 variants of this game are the 1, 2, 3 or 4 pouch variants, where only 1, 2, 3 or all 4 pouches can be used for pocketing coins, and the disallowed pouches (if any) are blocked by magnetic traps. 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.

3. Dynamic Composite Aggregates: Forming, Breaking, and Moving Them: 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, forming aggregates of coins. As such, the system of coins displays stable states (energy minima), which can be used to illustrate many concepts.

In Figure 6 (a), the attraction between coins offers the possibility of them forming interesting geometrical shapes - a linear chain (Figure 6 (a)), a tree (Figure 6 (b)), a dag (Figure 6 (c)), etc. In figure 6(a), Coin 100, coin 200, coin 300 and coin 400 forms a stable chain structure, with the magnet 300 of coin 100 attached to magnet 500 of coin 200. Magnet 700 of coin 200 is attached to magnet 900 of coin 300. Magnet 1100 of coin 300 is attached to magnet 1300 of coin 400.

In figure 6(b), the coins 100, 200 and 300 forms a non linear structure, with the magnet 300 of coin 100 attached to magnet 500 of coin 200. The adjacent magnet of the same coin, magnet 800 is attached to the magnet 1000 of coin 300.

In figure 6(c), the coins form another structure, where the magnet 300 of coin 100 is attached to the magnet 500 of coin 200, and the magnet 700 of coin 200 is attached to the magnet 100 of coin 300, thus forming a linear chain. The coin 400 is attached to the coin 200 by magnet 1000 of coin 400 and magnet 800 of coin 200 respectively.

The magnet 200 of coin 500 is attached to the magnet 400 of coin 300, etc. The entire game can be played with all or some 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 with respect to 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 7 (a) and (b) illustrates, the possibility of data storage using these magnetized coins. Data can be represented using the various configuration of coins. Two coins A and B, with the north of A sticking to the south of B, can represent a 0 (Figure 7 (b)), and vice versa for a 1 (Figure 7 (a)). In Figure 7 (a), the south of magnet 300 of coin 100 attached to the north of magnet 100 of coin 200 represents a data bit, 1. In Figure 7 (b), the north of the magnet 300 in coin 100 attaching to the south of magnet 100 in coin 200 represents a bit "0". As such, an interesting game can be just arranging the coins such that particular stable states ("data messages") are formed.

4. Use of Electromagnets:

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.

The magnetic field can be changed dynamically also during play.

5. Induction and Hysteresis Members

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.

6. Physical Obstacles

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 inelastic ally, depending on the material). The game then is played to go around these obstacles.

GAME DYNAMICS

Using one or more the infrastructures outlined above, very interesting game dynamics are created. Figure 11, 12 and 13 show various kinds of dynamics which we can encounter in this game, and make the game fascinating. These include the following:

• Figure 11 (a) shows a striker 100 hitting coin 200, leading to coin 200 being pocketed into pocket 400, along a straight path as in ordinary carom.

• Figure 11(b) shows a striker 100 hitting coin 200, leading to coin 200 being pocketed in pocket 400, using a curved path, due to deflection by magnet 300 below board surface. Magnet 300 has north pole on top below board, attracting south pole of magnet embedded in coin 200 at bottom. If the striker is magnetized, its path can be curved too.

• Figure 11 (c) shows a coin 200 being deflected away from pocket 400 by magnet 300 - this is a "swing" of the trajectory.

• Figure 11(d) shows a striker 100 hitting and bringing coin 200 near coin 500 at position 1100, followed by coins 200 and 500 aggregating to form aggregate 600 at position 2000 due to magnetic attraction between opposite poles, and translating and rotating as a unit (aggregate 600 in positions 2100 and 2200) after aggregation.

• Figure 11(e) shows a coin aggregate 600 breaking apart into two coins 200 and 500 after being hit by striker 100.

• Figure 11 (f) shows a coin aggregate 600 (triangle of 3 coins) breaking apart and reforming into a different aggregate 800 (linear arrangement of 3 coins), after being hit by striker 100. First aggregate 600 breaks up into a 2 coin aggregate 700 and a lone coin 200, which by magnetic attraction to a different magnet in the middle coin 300, forms the linear 3-piece aggregate 800. Note that middle coin 300 has 3 magnets, and different patterns can be made by attachment of coins to different magnets amongst these 3. Further changes to aggregate 800 (not shown) can occur due to collision with the board, another coin, etc. The breakup of aggregate 600 into aggregate 700 is exemplary, and may not happen in other situations.

Further examples are shown in Figures 12 and 13. In figure 12 (a) and (b), a tree is formed from a linear chain and a lone coin, and in Figure 13 (a) and (b), the tree is further modified to make a dag. The breakup and aggregation is a unique feature of magnetic carrom.

In Figure 12(a) Aggregate 700 is an aggregation of three coins, Coin 300, Coin 400 and Coin 500, in the form of a straight line in the upper left flank of the board and near to the Pocket 1400. Coin 200 is being targeted by Striker 1000 to hit the aggregate to form a new aggregate.

In Figure 12(b) Aggregate 700 is now re-aggregated to form Aggregate 800 along with the Coin 200 to form a tree structure. Due to the impact created by Striker 1000 on this new Aggregate 800, the entire aggregate is now subjected to a torque in the counter-clock-wise direction. Striker 1000 now is deflected away. Coin 100 is untouched.

In Figure 13(a) Aggregate 800 is now a collection of four coins, Coin 200, Coin 300, Coin 400 and Coin 500. Striker 1000 is now targeted to hit Coin 100 towards this Aggregate 800 still at the upper left flank of the board near to Pocket 1400.

In Figure 13(b) Aggregate 800 is now joined with Coin 100 to re-aggregate to form Aggregate 900. Due to the impact on the aggregation, Aggregate 900 is subjected to a Torque in clock-wise direction. Striker 1000 is in it's new position after the impact with Coin 100.

All these types of dynamics (among many others) make the game interesting. Based on these general considerations, a number of embodiments of this game, with varying pieces, carom sets, and board are described below.

SAMPLE GAMES AND RULES

Each magnetic carom game has one or more of special coins, strikers, and boards, and suitable rules. Below, we list some of the possible coin/striker types, pocketing rules, game rule bases and variants of magnetic carom.

DIFFERENT TYPES OF COINS

There are many different kinds of coins possible, and some exemplary embodiments are shown in the figures 14(a), 14(b) and 14(c). For clarity White is shown in light brown, Queen in Purple, and Black in Green.

1. Two Sided Double Pole White, Queen, Black (W2, B2, R2)
This coin has 2 magnetic ends, opposite to each other. The magnetic poles on each end can be the same (SS or NN), or opposite, as shown in Figure 14(a).

In Figure 14(a) coin 300, coin 200 and coin 100 have two magnets situated at diametrically opposite ends of the coin. Magnet 100 and 200 of coin 100 are positioned such that the north pole of magnet 100 faces outwards and the south pole of magnet 200 faces outwards. The coin 100 is in NS configuration (one pole is north, the other south). Magnet 500 and 600 of coin 200 are positioned such that the south pole of magnet 500 faces outwards and the north pole of magnet 600 faces outwards. The coin 200 is in NS configuration. Magnet 1000 and 900 of coin 300 are positioned such that the south pole of magnet 1000 faces outwards and the north pole of magnet 900 faces outwards. The coin 300 is in NS configuration.

2. Four Sided Double Pole White, Queen, Black (W4, R4, B4)

This coin has 4 magnetic ends, aligned at an equal spread of 90 degrees around the circumference of the coin. The magnetic poles on the end of the coin can be in any configuration, (for example NSSN, NNSN and so on), as shown in Figure 14(b).

In Figure 14(b) we show the embodiment where three coins, coin 100, coin 200 and coin 300 have 4 magnets placed around each coin at equal angular intervals. In coin 100, magnets 300 and 400 have south pole facing outwards and magnets 100 and 400 have north pole facing outwards. The coin 100 is in SNNS configuration starting clockwise from magnet 300. In coin 200, magnets 600 and 700 have north pole facing outwards and magnets 800 and 500 have south pole facing outwards. The coin 200 is in SNNS configuration starting clockwise from magnet 500. In coin 300, magnets 1200 and 1100 have north pole facing outwards and magnets 900 and 1000 have south pole facing outwards. The coin 300 is in SNNS configuration starting clockwise from magnet 1000.

3. Six sided Double Pole White, Queen and Black (W6, R6, B6)

This coin has 6 magnetic ends, located at an equal spread of 60 degrees around the circumference of the coin. The magnetic poles on the end of the coin can be in any configuration,(for example NSSNSS, NNSNSS and so on), as shown in Figure 14 (c).

Figure 14(c) shows the embodiment where three coins, coin 100, coin 200 and coin 300 have 6 magnets placed around each coin at equal spreads. In coin 100, magnets 100 and 300 and 500 have north pole facing outwards and magnets 200, 600 and 400 have south pole facing outwards. The coin 100 is in SNSNSN configuration starting clockwise from magnet 600. In coin 200, magnets 1800, 1500 and 1600 have north pole facing outwards and magnets 1300, 1400 and 1700 have south pole facing outwards. The coin 200 is in SSSNNN configuration starting clockwise from magnet 1700. In coin 300, magnets 1200, 800 and 1000 have north pole facing outwards and magnets 700, 900 and 1100 have south pole facing outwards. The coin 300 is in SNSNSN configuration starting clockwise from magnet 1100.

POCKETING RULES

The rules of magnetic carom are different from ordinary carom, due to the tendency of pieces to stick to each other. An exemplary embodiment of these rules is:

• For pocketing a single piece, same rules as that of ordinary carom game are followed.

• When the coins stick to each other, the rules change. The two examples in Figure 15 show first a 2-piece and then a 3-piece aggregate pocketed, as at least one piece is fully in the pocket area. Depending on the center of mass of the system, the collection may or may not tip over into the pocket, but the pocketing is valid in these cases as shown in Figures 15 (a), 15 (c) (both pocketed), versus 15 (b) and 15(d) (both not pocketed).

Figure 15(a) shows an aggregate 100, formed by the two Coins 100 and 200, both attracted and magnetically joined at the point Magnet 700 and Magnet 200. This Aggregate 100 is considered totally pocketed into Pocket 100 as one of the coin, namely Coin 100 is completely inside Pocket 100.

Figure 15(b): shows an Aggregate 100, formed by the two Coins 100 and 200, both attracted and magnetically joined at the point Magnet 700 and Magnet 200. Aggregate 100 is NOT considered pocketed into Pocket 100 as the none of the individual coins in Aggregate 100 is totally into Pocket 100.

Figure 15(c): shows an Aggregate 100, formed by the three Coins 100, 200 and 300, all attracted and joined at the points Magnet 800 and Magnet 200, and Magnet 600 and Magnet 900. This Aggregate 100 is considered totally pocketed into Pocket 100 as Coin 200 is totally into the Pocket 100.

Figure 15(d): shows an Aggregate 100, formed by three coins - Coins 100, Coin 200 and Coin 300 - all attracted and joined at the points Magnet 400 and Magnet 1200, and Magnet 800 and Magnet 900. This Aggregate 100 is considered NOT pocketed into Pocket 100 as no coin is fully in pocket.

SAMPLE GAMES

Below we specify several embodiments of the many rule bases of this game:

GAME1:

Use Basic Set 1: W2, R2, and B2, and 8 white and 8 black standard (standard non-magnetic carom coins).

Initial Coin Arrangement: Same as in carom, using R2 (Queen) in the center, and W2 and B2 sticking to it and to each other, making a triangle, and the rest of the initial position using the non-magnetic standard coins. (Figure 16 (a))

In Figure 16 (a), we show the initial arrangement for Game 1. The queen is at the center and the black and white coins are arranged around the queen. In this particular configuration, Coin 100, Coin 200 and Coin 300 form a triangle and are attached magnetically. All the other coins are non-magnetic and behave normally. The rules are as follows:

1. Coins have to be pocketed as in carom, and the first player to pocket all his/her coins wins.

2. Training sessions to learn the board are allowed (10 shots).

3. Striker orientation and which side is "up" can be changed during game by player.

4. Coin orientation (which side is up) decided at beginning, cannot be changed afterwards, except by normal play.

5. Coin or striker jumping out of the board causes the player to lose his/her turn.

6. Striker going into pocket causes the player to lose the turn.

7. Coins sticking to each other at same level (i.e. coins sticking to each other have the same height) cause no change in game.

8. Many interesting aggregates can be made by having coins stick to each other's sides, depending on the polarity of the magnets at the sides. Trees, Dags, etc can be built. These aggregates can be formed at the beginning of the play or dynamically during the game itself. In this case some embodiments of the relevant rules can be:

(a) Pocketing each coin individually wins the same points as in ordinary carom.

(b) Pocketing a whole aggregate (by pocketing any one of its constituent coins, without breaking the aggregate), wins the player, the sum of the points corresponding to all the constituent coins belonging to the player. All such constituent coins are removed from the board.

i. The turn is retained if all constituent coins belong to the player who played the turn.

ii. If the constituent coins include one of the opponents, the opponent also gets the points corresponding to his/her coins, and gets the turn.

(c) If the queen is included in the aggregate, it has to be "covered" by another coin of the same player. In this case the turn is retained.

(d) If the queen is included but not covered in a aggregate, then the opponent gets the points corresponding to the queen, and also the turn.

(e) A lone pocketed queen can be covered by a coin of the same player in the next turn, either solely or in another aggregate.

9. If coins jump over and stick to each other making a tower, then they will be disengaged, and placed in the center of the board.

10. If coins stick to each other and the striker, coins will be placed in the board center and the striker is given to whoever's turn it should be in normal carom (same player if at least one of players' coin has been pocketed, else the other player).

GAME 2

Use Basic Set 1: W2, R2, and B2

Initial Coin Arrangement: Same as in carom, using R2 (Queen) in the centre, and W2 and B2 sticking to it on opposite sides, and the rest of the initial position using the non-magnetic standard coins.

Figure 16 (b) shows the initial arrangement for Game 2. Here the queen is at the center and the black and white coins are arranged around the queen. In this particular configuration, Coin 100,

Coin 200 and Coin 300 form a straight line and are attached magnetically. All the other coins are non-magnetic and behave normally.

RULES:

Same as GAME 1, except for initial arrangement.

GAME 3

Use 6 Piece Set: W2,W2, W2, B2, B2, B2

Initial Coin Arrangement: Same as in carrom, using standard Queen in the center, and alternately

W2s and B2s ringing it all around, and the rest of the initial position using the non-magnetic standard coins.

Figure 16 (c) shows the initial arrangement for Game 3. Here the queen (non-magnetic) is at the center and the black and white coins are arranged around the queen (the queen is "trapped" and has to be rescued). In this particular configuration, coins Coin 100 ~ Coin 600 form a circle and are attached magnetically. All the other coins are non-magnetic and behave normally.

RULES

Same as GAME 1, except for initial arrangement.

GAME 4

Use Basic Set 1: W2, R2, and B2

Initial Coin Arrangement: W2 on left flank centre, R2 in the centre, and B2 in the right flank centre, as shown in Figure 16 (d).

Figure 16 (d) shows the initial arrangement of Game 4. We have three Coins, which are a White coin, Coin 100 at the center of the left flank, a purple coin (queen), Coin 200 at the center of the board and a Black Coin at the center of the right flank. Some of the possible shapes that can be formed are a triangle, straight line and a line which is at some random angle.

RULES:

1. Coins have to be made to stick to each other, forming one of several shapes

1.1 Triangle: W2 R2 B2
1.2 Straight line: W2 - R2 - B2
1.3 Angle: W2 - R2 - B2

2. Players play in rounds, each player getting upto 10 shots per round.

2.1. There are upto 10 rounds in the game per player.
2.2. Each player has to make one of the above three shapes, by manoeuvring the pieces so that they form one of these shapes.

• Triangle wins 10 points

• Straight line wins 5 points • Angle wins 10 points

3. At the end of 10 rounds, the player with the maximum number of points wins the game.

3.1 In the case of a tie, additional tie-breaker rounds are played till the tie is broken.

4. In each tie-breaker round, a triangle has to be formed. The player who uses fewer shots wins the tie-breaker round and the game.

4.1. If after 10 tie-breaker rounds, the score is even, the game is drawn.

5. If a coin is accidentally or otherwise pocketed, the respective coin comes back to its original place on the board, and the turn is lost.

OTHER SAMPLE GAMES

Some more examples of the immense possibilities of magnetic carom are shown in the figures and rules given below. For example, the initial arrangement can be changed. One possible set of coins is shown in Figure 16 (e). The queen is at the center and the black and white coins are arranged around the queen. The magnets of coins are in an alignment such that this configuration is stable. For instance the north pole of magnet 100 of coin 100 is attached to the south pole of magnet 1000 of the coin 400, and so on. The queen configuration here is NSNSNS. At multiple positions, the magnets of a coin are attached to other coins' magnets.

Figure 16 (f) shows another configuration. The queen is at the center and the black and white coins are arranged around the queen. The magnets of coins are in an alignment such that this configuration is stable. For instance the north pole of magnet 100 of coin 100 is attached to the south pole of magnet 1000 of the coin 400, and so on. The queen configuration here is NNNSSS. At multiple positions, the magnets of a coin are attached to other coins' magnets.

The initial position is stable. A very large number of variants of this initial position can be generated by flipping the polarity of one or more of the pair of magnets facing each other. This offers a very rich set of games, generatable by just flipping polarities. A kit of magnetized coins can be provided for this purpose, and selected at the beginning of the play. Selecting a set of coins, which can make a stable initial position, is itself a challenging exercise and can fetch bonus points in play. If the player cannot select such a stable position, a default one is used.

The changed magnetization of the coins changes the dynamics and offers in principle a whole universe of games to play. As another variant, the aggregates should not touch the board sides, else we get a penalty. The game then is to make the aggregates move in every stroke without touching the sides, else we change the turn. There are clearly many variants possible on this theme.

Some more variants are described here. Unless otherwise indicated, the initial position of the coins is as per normal carom.

• Single Coin Game: Here in Figure 16(g), Striker 100 hits coin 500 which follows the path shown by arrows and hits coin 200, which will be pocketed.Here the presence of barriers (attractive or repulsive) prevents a direct shot from being taken (unless a very high degree of mastery is achieved, to exploit the magnetic barriers). The game is to put the coin in a pouch, with the minimum number of trials. If the number of trials of both players is the same, then the tie can be broken by looking at the distance travelled by the striker/coins, the number of rebounds, the energy expended in the process, etc. The initial position of the coin can be anywhere on the board. An optimal solution to this problem involves a lot of mathematics and physics, and can be quite instructive. This game clearly generalizes to any number of coins.

• Only Striker Magnetic: In Figure 16(h), another simple version of this game is one in which only the striker 100 is magnetic (monopole/dipole/tripole etc), together with some magnets in the boards. Here only the trajectory of the striker needs to be carefully determined. The amount of magnetic "swing" can be varied between strikers, ranging from a non-magnetic striker to a striker having a powerful magnet. This offers varying amounts of difficulty in playing this game, with magnetically more powerful strikers yielding more points. Another variant of this game can offer the player the option, of replacing a magnetic coin, with an easier to play non-magnetic one, offering less points and vice-versa. The rules can be exactly the same as in normal carom.

• Magnetic Brake: An aluminum flat section 200 is inserted in a slot below the surface (it is not visible from the top). Then a magnetic striker 100 is used to hit a coin, which is on the opposite side of the aluminum flat. The induction forces cause the striker and coin (if magnetic) to slow down at the section. As showin in Figure 16(i), Striker 100 when moves through the induction member 200 experiences decrease in velocity and strikes coin 300 with lesser velocity .This is a fun game illustrating principles of magnetic induction, conductivity, etc.

The game can be repeated with flats, and non-magnetic strikers and/or coins, which can be monopoles, diploes,etc. The full game can be played with a number of flats inserted, offering inserting challenges to the players. A Variant is to accurately detect the presence of the hidden flats in the board (and their thickness and material), just from velocity measurements. This can be done with a high-end version of the game, with a camera and an algorithm, which detects changes in velocity. This is an excellent device for learning electromagnetism.

• The magnets yielding attractive/repulsive areas can be placed at various places on the board, exemplarily making areas like the center, the pouches, the middle of the home positions, one or more ends, etc hard to negotiate. If a very high degree of skill is achieved, then these areas can be used to advantage to maneuver the striker/coins, analogous to interplanetary probes utilizing the gravitational pull of planets to advantage in their journey.

• The striker/coins can be made active, exemplarily using linear motors embedded in the board, inducing eddy currents/magnetic forces on the striker-coins. Then an active game can be played, with the striker programmed to put the coins into the pouches, and the coins trying to get out of the way

The same principle can be used to enhance any board game like snooker, billiards, etc. For Eight-Ball, the 8-ball, together with the board can be magnetically enhanced, with embedded magnets/induction/hysteresis members, and the ball can swing past repulsive areas and get attracted to attractive areas (traps). A snooker table is shown in Figure 17, with the coloured snooker balls 100 (six of them) being magnetized. Balls in these magnetically enhanced games can swing by repulsive areas, get trapped in attractive areas, form aggregates by attraction, reform aggregates during impact, etc. Essentially, the magnetic enhancement to the coins /balls enables makes them behave like atoms, capable of forming molecular aggregates during close approach of these "atoms", splitup of these molecular aggregates in collisions, etc.

FURTHER EXTENSIONS:

The game as described can be further extended in many ways. Software can be created to setup and/or play this game, which can do one or more of the following:

1. Calculate new patterns of magnetization (striker, coins, board), which can be set using either a different striker, coins or board, or with special coils to change the magnetic field at various positions, to offer games with various degrees of difficulty.

2. Offer a completely online game, where the game is played on the computer only.

3. Monitor the speed/velocity of striker/all coins using a camera, for input to educational software illustrating mechanics and electromagnetism. The position and velocity of striker/ each coin can be tracked.. All collisions can be tracked. Energy, momentum, angular momentum, position of center of mass, etc can all be computed and displayed on the computer screen.

As shown in Figure 9, a webcam scans the coins on board and analyzes the linear and angular momentum of each coin. In each collision, the exchanges of these quantities amongst the colliding coins can be shown. Energy loss due to friction losses at each position can be shown on the screen.

If there are eddy and/or hysteresis losses induced due to the presence of conductive material under or near the board, this can be illustrated too. The difference in loss between a magnetic dipole (Figure 10) and a monopole can be shown, etc.

All in all, the camera converts this game to a physics laboratory, and has extensive educational and entertainment value.

4. Control a "robotic actuator", which has a physical actuator, capable of launching the striker.

An algorithm to control the speed and direction of the actuator is required. This algorithm can be as sophisticated as one desires (simple versions of this problem are NP-Hard), since it is a path finding with soft obstacles.

5. Figure 18 (a) shows a picture of Automatic Carom Player which has a very simple device where a reciprocating piston hits coins on a tilted board. Guides are present to direct the coins back to the piston for continuous play. More sophisticated versions can be built with closed loop control and sensors to detect coins, and optimally hit them.

6. Use an "active striker", which has inbuilt power, and programmatically control it to automatically strike coins. The striker to pocket all the coins first is the winner. Alternatively, the striker, which uses minimum energy, is the winner.

HARDWARE EMBODIMENTS:

Here we list a number of exemplary hardware embodiments for the coins and/or strikers and/or board. The coin material need not always be wood. Different materials can be chosen for the striker/coins, and used together with possibly hollow unfilled areas, so that the coin/striker has the same mass as a normal carom coin/striker. By proper construction, the center of mass of the coin/striker can be kept the same as a normal carom coin/striker, at the center. The coefficient of elasticity can be controlled by appropriate choice of materials and manufacturing. Each coin/striker can then be so manufactured that the same kind of elastic collision happens, irrespective of where it is hit by the striker or another coin. A plastic coin with embedded magnets can also be made to have the same collision dynamics as standard wooden coins.

In Figure 8, the 3-D magnetic field distribution around coin 100, produced by the embedded magnet 100, is carefully specified to yield a certain dynamics in the presence of other magnetized/hysteresis/induction members. The maximum field extent can be tailored to be acceptably small, for safety. Instead of a magnet, the coin/striker/board can have induction/hysteresis members.

An exemplary design for a coin (made of plastic or wood) has magnetic pieces inserted and glued into holes in the sides, with a tape wrapped around it. The tape is thin - around 60 microns - and helps together with the glue to both keep the magnets inside the holes, and provide a small amount of cushioning for the impacts experienced during play. The thinness of the tape ensures that the magnetic force exerted is not significantly reduced compared to that exerted by magnetic pieces directly contacting each other. Figure 19 shows the picture of the Magnetic Carom Coin with six dipolar magnets and transparent tape covering them.

Given good manufacturing, the optimal play will not vary between coin to coin of the same kind, and can be learned by human beings, or by a computer program.

WE CLAIM

1. A board game characterised with magnetic properties including at least any of the following accessories:

a. A magnetically enhanced table;

b. A magnetically enhanced striker; and

c. A magnetically enhanced coin wherein magnetic enhancement of said table, striker, or coin, is achieved by placing a magnet or a conductive substance, or a ferromagnetic substance inside or on the surface of the said table, striker or coin.

2. The game of claim 1 wherein it is a game of a carom.

3. The game of claim 2 wherein the coins and striker are magnetically enhanced, and the table is not magnetically enhanced.

4. The game of claim 2 wherein the board and striker are magnetically enhanced, and the coins are not magnetically enhanced.

5. The game of claim 2 wherein a coin is enhanced with 2 magnets touching the side surface, placed diametrically opposite and embedded into the coin.

6. The game of claim 2 wherein a coin is enhanced with 2 magnets touching the side surface, placed diametrically opposite and embedded into the coin, and having a magnetic field pointed in the horizontal and radial direction parallel to the board.

7. The game of claim 2 wherein a coin is enhanced with 4 magnets touching the side surface, and embedded into the coin and placed ninety degrees apart.

8. The game of claim 2 wherein a coin is enhanced with 4 magnets touching the side surface, and embedded into the coin and placed ninety degrees apart, and having a magnetic field pointed in the horizontal and radial direction parallel to the board..

9. The game of claim 2 wherein a coin is enhanced with 6 magnets touching the side surface, and embedded into the coin, and placed sixty degrees apart.

10. The game of claim 2 wherein a coin is enhanced with 6 magnets touching the side surface, and embedded into the coin, and placed sixty degrees apart, and having a magnetic field pointed in the horizontal and radial direction parallel to the board.

11. The game of claim 2 wherein a coin is enhanced with a magnet touching the surface of the coin, and a plastic seal is applied over the exposed surface of the coin.

12. The game of claim 2 wherein pieces stick to or repel each other, due to the magnetic attraction and repulsion.

13. The games of claim 1, which is a game of snooker, with the coloured balls magnetically enhanced.

14. A computer program product which enables the game of claim 2 to be played on the computer, with software to simulate the dynamics of the pieces of magnetic carom, striker, coins and board.

15. The game of claim 2, wherein a first carom coin can attach itself to a second carom coin, and the two move together with translation and rotation as an aggregate.

16. The game of claim 2, wherein an aggregate of at least two carom coins, can break up into two parts moving separately with translation and rotation.

17. The game of claim 2, wherein an aggregate of at least two carom coins, can change shape, while remaining a single aggregate.