US3550943A - Apertured board and marker game apparatus - Google Patents

Description

United States Patent [72] lnventor John B. llatcher 3104 Silver Lake Road, Minneapolis, Minn. 55418 [21] Appl. No. 623,578 [22] Filed Mar. 16, 1967 [45] Patented Dec. 29, 1970 [54] APERTURED BOARD AND MARKER GAME APPARATUS 11 Claims, 11 Drawing Figs.

[52] US. Cl 273/131, 273/ 136 [51] Int. Cl A63f 3/02 [50] Field ofSearch 273/130, 131,134,135,136,139

I 56] References Cited UNITED STATES PATENTS 1,988,301 1/1935 Coffin 273/136 2,463,425 3/1949 Rendel 273/136 2,575,269 11/1951 Hall 273/130 ///I "0/ III/l Primary Examiner-Delbert B. Lowe ABSTRACT: A two-sided game board with various markerhole combinations, in which positions on both sides of the board are identified with markers, which are pushed out from the opposite side in the course of play. With large open holes, markers shorter than the hole inserted in one side conceal the movement and position of markers on the opposite side; single markers with one end identical can also be used. With long, small holes, markers which extend to within a few diameters of the end of the hole can be used, and both hole and marker may be made a dull black for even more effective concealment of the presence or absence of the marker from the op posite side. Gravity or spring restrained balls, or crooked holes, with flexible markers, are shown, as well as curved holes with correspondingly curved markers.

'PATENIEU UED29 197s QIIllllllllllllIlllllllllllllllllllllllllll SHEET 1 OF 2 "III/1 1111111170? .l/Il'i,

INVENTOR.

APERTURED BOARD AND MARKER GAME APPARATUS ABSTRACT OF THE DISCLOSURE A two-sided game board with various marker-hole combinations, in which positions on both sides of the board are identified with markers, which are pushed out from the op posite side in the course of play. With large open holes, markers shorter than the hole inserted in one side conceal the movement and position of markerson the opposite side; single markers with one end identical can also be used. With long, small holes, markers which extend to within a few diametersof the end of the hole can be used, and both hole and marker may be made a dull black for even more effective concealment of the presence or absence of the marker from the opposite side. Gravity or spring restrained balls, or crooked holes, with flexible markers, are shown, as well as curved holes with correspondingly curved markers.

This invention is a novel apparatus for playing various old and new games, and demonstrating various tests of probability theory. It is well known that there are interesting games which require complex scoring or checking procedures, or depend on pencil and paper recording, or which require a referee or neutral person to transmit only a certain portion of the play information between the players. Such complexities are practical problems in that they make the games unpopular, or not readily playable. My apparatus solves such problems, and permits direct, simple, two-person or two-team play of nearly all such games. Further, there are a wide variety of what are now typical board type games, or pencil and paper type games which, adapted to my apparatus, become new and fascinating games. And finally, there are entirely new and novel games which have not (indeed could not have) existed before the invention of my apparatus and which can now be played.

The purpose of my invention is to provide a simple, direct, automatic scoring and play method for many types of games,

so that the players can concentrate on the game and its strategy; a further object is to provide an apparatus which makes it possible to play entirely new types of games not hitherto possible; and finally, a further object is to provide an apparatus for the direct testing and educational demonstration of certain probability models.

The broad utility of my basic invention is that it permits a wide variety of minor design modifications, and also that it can be used to play a large number of games of widely different types. To illustrate this in complete detail would require describing separately for each one of a large number of games a set of the many possible minor adaptations of the basic apparatus, which would run to many pages and be unnecessarily repetitive to one skilled in the art of game design. Hence I will describe some three representative old games, one new game, and a probability demonstration, with each utilizing a suitable apparatus modification, with commentsas to other possibilities. It will be noted that it is obviously possible to adapt any game to any of the apparatus modifications, simplifications, size changes, patterns, etc., a skilled designer might choose one or another variation on the basis of some subtle appeal or adaptation to a particular manufacturing process; in this respect the choices are merely examples of my own preference. Further, the particular games used for illustration are but representative of many, and were chosen on the basis of permitting clear, simple, and complete description of play and the teachings of my invention, and revealing and utilizing as simply as possible a large number of the possible inherent and unique design variants of my invention.

In all of my descriptions, the labels, names, symbols, etc., are chosen merely for convenience in describing the use of the apparatus in the various examples of games. As is well known to game designers, any specific set of equipment and rules can be described abstractly, as by a mathematical model, and it can be adapted to represent various and many subjects, in the sense that the coloring, ornamentation, shape, configuration, patterns, and labelling of actual game equipment may be made representative or models of different sets of real world things, and the play of the game can be described so as to represent transactions or actions related to such real things. My descriptions are not intended to indicate or suggest any limitation in such application of the apparatus to such referents as may be used to keep the descriptions simple and lucid.

In brief summary my invention consists of a board or playing field which is used from both sides, with markers adapted for insertion in suitable apertures extending through the board, permitting concealment of the markers on each side from the opposite side, except as disclosed during the course of play of a game or specific demonstration when the markers are pushed out, by means of appropriate combinations of apertures and markers.

FIGS. 1 and 2 show an external view of a typical set of apparatus, and FIGS. 3-41 show cross-sectional views of variousmarker-aperture combinations.

The test or playing field or board 1 consists of any suitable pattern or layout of a multiplicity of openings or apertures extending through the board. The board is shown in a vertical position, through the basic concept is not limited to such posi tion. The apertures may be arranged in any pattern or layout desired, to suit a subject or game application, such as a picture or other representation, and more or fewer openings may be provided for any particular game. For convenience the board is shown with a square grid or array of 36 apertures, in six rows and six columns. Each aperture 2 may be of whatever shape desired, such as triangular, square, etc., and is conveniently shown as a simple round hole, several times longer than its largest cross-sectional dimension. A suitable baffle, shown in FIG. 1 as a removable drawer 3, which; can extend beyond the face of the board on either side, is sometimes used. Finally, a set 'or sets of a multiplicity of appropriate marker pieces, which can be placed in the apertures, are provided. Typical samples of these marker pieces are conveniently shown as simple round pegs in FIG. 2, numbered from 4 through 16 and in various alternative forms in F108. 5 through 9 numbered 20- --24 inclusive. These marker pieces are of various lengths and shapes and identified by various colors, and in some cases they may be pushed all the way through the apertures, and in other cases can only be inserted part way, all depending on their specific use as will be described in detail in the various game examples below. While shown here as simple round pegs, distinguished only by color in some cases, in almost any specific game they would be configured and differentiated by representation compatible with the game subject."

As will be indicated in the detailed discussion of specific examples, there are various particular features, both useful and novel, of the apparatus. But an important basic general feature, common to all specific uses, is readily apparent: In any game the opposing players make their" choices, strategy, and moves by placing or pushing through various markers from opposite sides of the board. And while each player has complete and direct information as to his own play, position, etc., at all times, he has only a portion (in some cases none) of the information as to his opponents play, strategy, disposition, etc., because he does not seehis opponents side of the board. Thus a strong element of chance, and a requirement for searching," are introduced into the basic strategy of the game. But at the same time, the partial resultsof a players particular actions or play are available directly, in terms of the opponents pieces or markers he does (or does not) push out.

This information, the equivalent of tedious scoring in some games, and an entirely novel feature of a board-type game, provides various clues as to the opponents position, strategy, or play, and permits the adoption and shifting of particular strategy or play. The result of a particular move or piece placement may be immediate, in terms of seeing the piece knocked out immediately when no baffle is used, or, with the use of the baffle or drawer, it may be deferred until after some particular event or sequence of moves or completion of a turn. Many of the games played with my apparatus are of this search-strategy type, in which particular patterns or spatial arrangements are developed and manipulated by the players, with the eventual outcome of the game depending on this, as well as searching for and discovery of the opponents pattern or position. Almost any standard board-type game which involves patterns, paths, and the movement of pieces can be made into a search-type game, simply by concealing from each player some or all of the disposition, arrangement, or location of his opponents counters, pieces, etc.

For specific exemplification of my apparatus, 1 will describe in detail the games called Salvo and Moving Salvo, which heretofore have been known primarily as complex paper and pencil games, and Simplified Kriegspiel, simplified from the board game which requires a neutral referee in addition to the two players or teams. I will also describe, as particularly illustrative, the totally new game of Maze which I have invented and which cannot be played by two players except with my apparatus, and finally, I will give an example of a probability demonstration. As is well known, there are frequently many different versions of a game, depending on the particular, specific rules of play which are adopted. The elaboration of detailed rules is not pertinent to the subject of this specification, so in all cases only the simplest essentials of a set of rules which provide for a playable game, and which illustrate a use of my apparatus, are described.

The game Salvo has long been know, under various names such as Battleship, Ships, Fleet, etc., and has been mainly played with pencil and paper, with a complicated process for scoring and play based on (a) the calling of coordinate locations back and forth between players, or on (b) a considerably simpler version utilizing carbon paper. With the apparatus I have invented, it becomes an even more simple and playable game.

The game typically simulates a naval battle, with ships of two opposing fleets hidden from each other firing "shots in groups (salvos), attempting to hit each other. It is convenient to adopt this model in the description, though obviously many other real world situations, involving armies, expeditions searching for something, etc., could also use nearly identical rules and play, merely with different associative names, labels, etc.

In playing this game with my apparatus, two boards similar to that illustrated by FIG. 1 are used and represent the opponent players oceans, with the apertures, illustrated in the form of holes, being positions in the oceans. Marker pieces in the form of round pegs such as are shown at 4, 5, 6, and 7 in FIG. 2 are placed in the holes to indicate the positions of ships, shots in a salvo, etc. The blue pegs 4 represent ocean; the red pegs 5 represent shots, and the two colored pegs 6 and 7 represent portions of a ship; in this version the half green, half bue pegs 6 represent submarine parts, and the half orange, half blue pegs 7 represent parts of a cruiser. The pegs 4, 6, and 7 are as long as the depth of the holes (the thickness of the board), so that when inserted in a hole they are flush with the board surface on each side; the pegs 5 are conveniently about one and one-fourth times as long, so that they project slightly.

The board may have as many holes as desired, and they may be in any configuration or array, as, for example, to conform to a map. In general, the larger the number of holes the longer the game, and it has been found that for an array or pattern of n holes, each player should have, initially, ship pegs equal to one and one-third times the square root of n as a preferred ratio of ship pegs to ocean positions for a good game. For the example game here, we will assume a 6x6 array of 36 holes, and a total of eight ship pegs for each player. Each player will have three ships; two submarines, each represented by two adjacently placed half green pegs 6, and one cruiser, represented by four half orange pegs 7, which must be placed adjacent to each other and in a straight line. Each player has a supply of red shot pegs 5 equal to the number of holes in the board less the number of ship pegs 6 and 7 he begins with.

Before beginning play, each player places his ships" on his own ocean by inserting his ship pegs band 7 in the hole positions he chooses in his board, with the blue ends away from him, as shown in FIG. 10, and he then fills the remaining holes in his ocean board with the blue ocean pegs 4. He knows where his ships are, because he can see the colored ends of the pegs, but his opponent, seeing during the game only the opposite blue ends of the pegs, does not, since the blue ends of the pegs 6 and 7 are exactly the same color as the all-blue pegs 4 which fill all of the remaining holes. When each player has thus filled his board, the two boards are set side by side and between the players, so that each player can see his own ships, and his opponents ocean.

Each player now fires his first salvo on his opponent's ocean, attempting to locate his opponents ships. Each player has a number of shots on this (or any other) salvo equal to the number of his own ship pegs remaining in his own ocean board; for this first salvo this will be eight. So each player takes eight of the red pegs 5, and inserts them in the holes of the opponents ocean board where he thinks his opponents ships might be. While he is doing this, the drawer 3 is pushed back towards the opponent, so that as a player inserts pegs, the pegs displaced from the holes fall into the drawer, but the player pushing them out cannot yet see them. After both players have fired their complete salvo, they then open the two drawers and observe what hits they have made, simply by noting if any of the opponents ship pegs 6 and/or 7 are in the drawer.

Both players then fire another salvo, of the proper number of shots, and learn what they have hit, and so play continues until one of the players has completely sunk his opponent's fleet and wins. The basic strategy of the game is to appropriately group the shots on each salvo, so that if a hit' is obtained, the location of the remainder of the ship which was hit is easy to find on the next salvo, and so on.

The key features of importance with respect to my apparatus are: There is no paper work, or calling of numbers, and no possibility of scoring errors, with a completely reusable apparatus. A player can, at any time, see his own fleet, and thus he knows exactly how many ships he has left, and what ships he has hit on each salvo are directly observed by noting the colors of the pegs in the drawer, and he can stack them up to keep track of his hitsin any way he chooses, and can check directly how many shots his opponent has left. Indeed, in an advanced version of the game, more suitable for play with a large 12x12 array board, the red shot pegs 5 would be provided with salvo numbers on the ends, so that a player can keep track of his past salvo patterns easily. A good game on this larger board involves each player starting with 16 ship pegs; the ships could include a destroyer (three holes long), and a battleship (five holes long) in addition to the ships described for the example game above.

Moving Salvo is another version of the basic Salvo game, which has the additional feature that each player can move his ships during the game. As played with pencil and paper it is so very complex that it is seldom played, but it is quite simple and direct with my apparatus. In a version quite similar to the Salvo described above, it utilizes the markers 5, 8, 9, l0, and 11 shown in FlG. 2. The green and orange ship marker pegs 8 and 9, and the blue ocean peg 11 are shown in a convenient form with an enlarged head which will not go into the hole; the portion which does enter the hole is just less than one-half of the hole depth, and the blue ocean peg 10, which completely enters the hole, is also just less than one-half of the hole depth.

In Moving Salvo the play is essentially as in the regular Salvo above, except as follows: Before placing his ships initially, a player first puts into every hole position the half length blue pegs 10, and then he inserts the appropriate pegs 8 and 9 which identify his ships, as shown in FlG. 11, and finally he fills all of the remaining half filled holes with the all blue half length ocean pegs ll. As in regular Salvo, each player can see his own ships, but only blue pegs are visible to his opponent on the opposite side of the board. As in standard Salvo, each player fires as many shots on each salvo as he has unhit ship positions. When the players have completed their salvos, by inserting red shot pegs 5 in various holes, and pushing out whatever is in those holes, and have learned from the contents of the drawers what they have hit, each player can, if he chooses, move each of his ships on his own board or ocean.

A player can move each of his ships one hole into any ad jacent position which is not occupied by a red shot peg, provided this does not bend" a ship from a straight line. To do this the player simply interchanges the half length blue peg 11 from the chosen new position hole and the half length ship peg 8 or 9 from the vacated position. The opponent cannot see the interchange or ship move because of the pegs 10, which are all he can see in any hole. And so each playercontinues to fire salvos and to move until one fleet is completely sunk. As in the standard Salvo, the object is to sink the opponent's fleet first, and the strategy is basically the same, with the added feature of the moving making it more difiicultto find the opponents ships.

In both of these games so far described, the half length and full length blue pegs l0 and 4 serve only the purpose of providing a uniform field to the opponent, so that he cannot determine the position or movement of a playeron the board; they can be thought of as blanking markers. There are other ways of automatically accomplishing this objective of concealment from the'opponent which make it possible to dispense with the use of blanking markers. One simple way would be to have the apertures themselves of very small cross-sectional dimension, but with a "relatively long length (the depth through the board), and'use markers which are less than the full length as shown in FIG. 6, where the diameter of the insertable portion of the marker and the aperture 2 is only about one-thirtieth of the length of the aperture.

Such a configuration makes it very difficult to see into or through apertures, and thus to detect whether or. not there is a marker in an aperture. Simple optical tricks, such as are shown in FIG. 7, with the inside of the aperture 2 and the inner end of the marker 21 painted a dull nonreflective black, will further decrease the possibility of detection of the presence or absence of a marker; thus when a marker is in the aperture there is less reflected light down into and back out of the blind hole, so the eye perceives essentially a dark circle of the aperture, and when the aperture is open, the lack of reflection of background light along the sides of the aperture decreases the effective illumination coming through the aperture, and provides a smaller image to the eye, so that open apertures also appear as a dark circle and similar to a filledaperture except when viewed from a very narrow angle close to their axes. For

adult games, and team'play, this would be entirely adequate,

as the tendency to try to cheat would be minimal.

Another way to conceal the position of one players markers is shown in FIG. 8; the aperture 2 is simply a crooked hole,

sufficiently displaced from a linear path so that the inner end of the flexible marker 22 is hidden from view. FIG. 9 is another example; here the aperture 2 has'a specific radius of curvature, so that the inner end of the marker 23 cannot be seen from the opposite side of the board. In this case the marker can be rigid if it has the same constant curvature as the aperture. In both of these cases it is possible to make certain that the markers inserted from-one side cannotbe seen from the opposite side under any conditions.

And finally, there is a wide variety of simple mechanical doors or obscuring mechanisms which could be placed in each aperture which would prevent seeing what, if anything, is in the aperture from the other side, but which can be readily moved aside when a marker piece is pushed into the aperture.

An example of a simple mechanical obscuring mechanism is shown in FIGS.'3 and 4, which are cross sections through the thickness of the board or playing field, of one aperture. In this case the aperture 2 is appropriately horizontal and has a vertical cylindrical enlarged space 17 near each end, the spaces being just large enough to contain the two spheres (typically marbles or common steel balls) 18 and 19, which normally test, under the force of gravity, on the bottom of the aperture (shown as a hole of circular ,cross section) as seen in FIG. 3 and keep the hole closed from each end. The diameter of the balls and the end shapes of the marker pegs are adjusted-so that when any marker peg such as 12 is pushed into the hole it will. readily push the ball 18 upward as indicated in FIG. 4; further, the pegs such as 12 usedwith this mechanism would be only so long that they could not touch the ball 19 which remains in place and keeps the aperture closed from the opposite side, as shown in FIG. 4. Thus while an opponent does not know whether or not there is a marker in the aperture, a second marker can be pushed into the aperture from the opposite side and it will push the first marker out. If the board is used in a nonvertical position, a spring could be provided to hold the ball to block the aperture. FIG. 5 shows the aperture pushed aside by insertion of the marker 24. If desired, a small groove 26 around the marker peg, opposite the ball when in a hole, would permit the spring-ball combination to hold the marker from falling out no matter what the position of the board. 1 i

All such design features which might be utilized for some particular game or configuration, or utilized for reasons of market appeal or manufacturing economy are compatible with my basic invention. The preference for any method of obscuring holes, to use or not use blanking pegs, is to a considerable extent dependent upon the specific game and its size; configuration, and application. Thus while the versions using blanking pegs described above in the, games of Salvo might be considered preferred for those two games, it would be perfectly possible to omit blanking pegs and adapt the game to use a large length/diameter ratio for the aperture holes, or to use a mechanism such as that shown in FIGS. 3

and 4. And similarly, the following games, which are described ,with three chess sets, and involves two players, each moving his own pieces on his own board, but neither of these players can see his opponents board and pieces. Areferee plays the actual chess game on a third board, which neither player can see, although the referee can see both players boards By appropriate verbal announcements the 1 referee keeps both players to moves legal in a proper chess game. A'simplified version of this game can be played with my apparatus, on one board, with only the players, on opposite sides of the board. It will be'described utilizing a board with round apertures which contain some simple obscuring device, of which that mechanism illustrated in FIGS. 3 and 4 might be typical.

The board would contain a square array of 8x8 or 64 holes, each representing one square on a standard chess board, and the marker pieces would be as illustrated in FIG. 2 by 12, I3, 14, and 15. The stem, or the portion of each of these pieces which can be inserted in the holes, is only about three-fourths of the depth or length of the holes, sothat when inserted they cannot be seen from the opposite side of the board. Each are inserted in the vertical row of the board which is at the left for each player, and in the order, from the top down, of two brown 14, four red 13, and two brown 114, and the four green pieces 12 are placed in the center four positions of the next row or column to the right. The various pieces can move, on each turn, as follows: The brown pieces can move along any diagonal, as many positions as desired, in a straight line. The red pieces can move either horizontallyor vertically in straight lines, as many positions as desired, and the green pieces can move in any direction, but only to the next adjacent position. No pieceican move over another, or into aposition already occupied on the same side of the board.

The object of the game is to capture fall of the opponents pieces. A piece is capturedwhen it is pushed outof a hole by an opponents piece from the opposite side of the board. The players move in alternate turns, moving one piece, as permitted by the rule for that piece, on each turn. If a green piece 12 reaches an opponents initial position (the last vertical row to the players right), it can be exchanged for an orange piece 15, which can similarly move in any direction, but can move as many positions as desired in a straight line on each turn.

Neither player knows, of course, the exact location of his opponents pieces, except at the start. But when a player moves to where an opponents piece is, thus knocking it out of the board and thereby capturing it, the capturing player knows what kind of a piece he has captured, because he can see it as it falls out of the board, and the opponent knows that the capturing player has a piece at that position. Good strategy is to maintain an interlocked pattern of pieces, so that when a piece is captured and lost at some particular position, the opponents capturing piece at that position can be immediately captured. The game I have called Maze" is a totally new game which .l have invented which utilizes the features of my apparatus invention', indeed the game cannot be played by two people or teams without it. The general idea of the game is the making of a trail or path through an unknown maze; each of the two players or teams first constructs a barrier which constitutes a maze which his opponent cannot see, and then each player attempts to trace a path across the board which avoids both his own and the opponent's barrier; the first player to succeed in tracing a complete path wins.

The version of the game described here is adapted to utilize a board with 144 apertures in a square arrayof 12x12, which has a convenient form of "blinding for example the apertures can be holes with a maximum diameter about one-thirtieth of their length through the board, and they are painted or otherwise finished inside with a dull nonreflective black finish or paint. Each player has 12 red pieces 13 called barrier pieces, and both players have access to a supply of green pieces 12 called trail pieces, red pieces called intersection pieces, and green pieces 16 called capture pieces. The insertable portion of the pieces 12 and 13 can project into the apertures only about three-quarters of the length of the aperture or hole, and the small ends are painted a dull black; their presence or absence in the holes cannot be determined from the opposite side of the board under normal playing conditions. The pieces 5, and the insertable portion of the pieces 16, are one and onequarter times as long as the holes are deep, so that when inserted they project through and are visible on both sides readily.

in the play of the game, the players first construct their barriers, or mazelike set of obstacles, by inserting, one at a time, in alternating turns, their 12 barrier pieces 13. lf either player on inserting his barrier piece knocks out the opponent's barrier piece already in that position, both pieces are removed and an intersection piece 5 is inserted at the position, and it now becomes the turn of the player whose barrier piece was knocked out. When all 24 of the two players barrier pieces are inserted (together with as many intersection pieces as may have been necessary), the players now attempt to construct or mark their trails. In this phase of the game, each player, in turn, places one trail piece 12 wherever he chooses. His object is to complete a continuous path or trail of adjacent pieces from the left to the right side of the board; the path may have turns, corners, or bends of any sort, but it cannot be broken or interrupted by his own barrier pieces 13 or by any intersection piece 5. Since a player does not know the position of his opponents barrier pieces 13, he will, from time to time, choose a hole position containing one. When he does, his trail piece 12 will knock out the opponents barrier piece, and when this happens, his piece is removed and another intersection piece 5 is placed in this position, and it is the turn of the player whose barrier was hit. it is also possible for a player to choose a hole where, unknown to him, his opponent has already placed a trail piece 112, and his trail piece will knock this out of the hole. When this happens, the player who inserted the last trail same as though his own barrier piece or an'intersection piep e is at the position, and will interrupt a continuous trail. Play proceeds in this way until oneplayer-successfully completes a continuous path or trail, and/or captures pieces, which extends from one side of the board to theother, when he calls win, and the board is turned around and his opponent can check that it is indeed a continuous and proper trail. To call win" without having completed a proper trail loses the game.

Strategy in this game consists of making good inferences as to the opponents barrier, from the pattern of intersection pieces that can be observed, as well as to the opponentstrail path as found by trail piece captures. If an additional rule is made that the initial barriers must also consist of adjacent pieces, there is then a great deal of information that makes the game very satisfying to analyticallyinclined players.

As an example of a probability exercise, or demonstration, consider the general case of the probability of repeated trials of some event of known probability or chance. Thus one can compute the probability of finding a set of randomly placed items, in a number of trials, just as one can compute the probability of success in drawing unseen marked balls from an urn containing a known composition of marked and unmarked balls. Applied to my apparatus, it is considered, for example, that eight items are hidden amongst 144; this can be modelled with my apparatus by randomly placing eight of the one end colored marker pegs such as 6 or 7 in a board of 144 apertures, with the rest of the board filled with plain blue markers 4. If the board is now turned around, so only the plain blue ends of all the pegs are visible, and the locations of the pegs are unknown, a series of tests can be made attempting to find them. Suppose a test consists of 18 trials; that is, 18 pegs will be pushed out with say 5 red ones; the result of each test is how many of the eight colored ones are found. The pegs could then be restored to their original positions, and a second and then a third, etc., test of 18 trials could be made.

Mathematically one may compute the probability of finding some number k of the eight hidden markers during any particular test. In the table below, the results of such a calculation are given; the last line of the table gives the average of some 20 such tests made using a model of one form of my apparatus.

Number of successes, k, or page found O 1 2 3, 4

Calculated probability, P(k) of finding k 34 40 .20 05 01 Average of 20 tests made with appuratus .30 .45, 15 10 00 I claim:

1. In a game or educational apparatus, the combination of a board or playing field, uncovered on both sides, having a multiplicity of continuous, open apertures extending through the board, together with various markers which can be inserted into any of the apertures from either side of the board, and means, continuously and repeatably usable throughout the game or demonstration, for preventing the presence or absence of a marker inserted or not inserted in an aperture from one side of the board from being readily detected from the opposite side of the board, while maintaining the board in an uncovered condition.

2. The elements of claim 1 in which the means comprises said apertures being very long with respect to their maximum cross-sectional dimension, said markers shaped to limit their insertion to such an extent that when a marker is inserted as far as possible into an aperture its inner end cannot be readily seen from the opposite side of the board.

4 3. The elements of claim 2 in which the interior of the apertures and the inner ends of the markers are made with surfaces that provide a visually effective means which makes it difficult for a player to detect the presence or absence of a marker which has been inserted or not inserted in an aperture from the opposite side of the board.

4. The elements of claim 3 in which the means comprises surfaces of the interior of the aperture and the marker that provide a low optical contrast ratio between them.

5. In a game or educational apparatus, the combination of a board or playing field, having a multiplicity of apertures extending through the board, together with various markers which can be inserted into any of the apertures from opposite sides of the board; each of said apertures containing adjacent its ends moveable obstructions eachof which effectively conceals the central portion of the aperture and which can be readily pushed aside by a marker as it is inserted, and means subjecting them to a force that returns them to their original position when the marker is withdrawn; and said markers being shaped so that the inner end of the insertable portion cannot extend into the aperture past the opposite end of the concealed central portion when the marker is inserted into the aperture as far as possible. 7

6. The elements of claim 1 in which the means comprises said apertures having longitudinal axes which are not straight lines through the board, said markers having an insertable portion sufficiently flexible to follow the nonlinear path, and being shaped to limit insertion to such an extend that when a marker is inserted from one side of the board as far as possible into an aperture its inner end cannot be readily seen from the opposite side of the board.

7. The elements of claim 5, in which the obstructions are balls positioned transversely in the aperture by springs constituting said subjecting means and in which each marker has an indentation positioned along the insertable portion at a position such that when the marker is positioned as far as possible in the aperture the nearest ball seats in said indentation.

8. In a game or educational apparatus, the combination of a board or playing field, uncovered on both sides, having a mul' tiplicity of continuous, uniform, open apertures extending through the board, together with various markers which can be inserted into any of the apertures from either side of the board, and means, continuously and repeatably usable throughout the game or demonstration, for preventing positions on the board which are identified by particular identifiable markers inserted in the apertures from one side from being identified from the opposite side, while maintaining the board in an uncovered condition.

9. The elements of claim 8, in which; the means comprises a set of markers which substantially fill each and all of the apertures and have one end separately distinguishable and their other ends identical, in combination with a second set of markers, each of which also substantially fills an aperture.

10. In a game or educational apparatus, the combination of a board or playing field, uncovered on both sides, having a multiplicity of continuous open apertures extending through the board, together with markers for use at one side of the board which are separately identifiable and .which are less than the length of the apertures, in combination with a second set of markers which are identical to each other and each of a size to substantially fill the remaining portion of an individual aperture which is occupied by a marker from the first set, with said second set being placed in substantially all of the apertures on the opposite side of the board, and concealing the first set.

11. The elements of claim 1 in which the means comprises said apertures having longitudinal axes: which are a particular curve with a constant radius of curvature, and said markers having an insertable portion of the same radius of curvature and particular curve, said insertable portion being defined as to length by a suitable projection limiting insertion to such an extent that when inserted as far as possible the inner end thereof cannot be readily seen from the opposite side of the board.

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