US3460835A - Apparatus for playing a mathematical board game - Google Patents

Description

Aug. 12, 1969 o. E. CRANS 3,460,835

APPARATUS FOR PLAYING A MATHEMATICAL BOARD GAME Filed Aug- 22. 1966 2 Sheets-Sheet 1 24 nun wu sconms mm. POINTS no-n4 ITS-I80 s I65-l69 lBl-IBS 4 160-164 use-I90 3 459 I9l-l95 --2 :54 I96-200 INVENTOR. DAVID E. CRANS FIG.3 (P A UNDER I50 0R OVER 200"--O Filed Aug! 22 1966 Aug. 12, 1969 I v o. E. CRANS v 3,460,835

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' INVENTOR. DAVID E. CRA NS 'r'ron EYS 3,460,835 APPARATUS FOR PLAYING A MATHEMATICAL BOARD GAME David E. Crans, 1149 N. Old Manor, Wichita, Kans. 67208 Filed Aug. 22, 1966, Ser. No. 573,942 Int. Cl. A63f 3/00, 9/06 US. Cl. 273135 3 Claims ABSTRACT OF THE DISCLOSURE Various types of numerical games are known to the prior art using a plurality of numbered pieces selectively placed on a given game board in a certain order to indicate ones skill. However, the prior art devices are used in a manner to indicate ones skill in multiplication, subtraction, or the like and are not operable in a manner requiring one to foresee innumerable combinations of present and future plays to pit one players skill against anothers similar to a game of chess.

In preferred specific embodiments of the invention, a mathematical game is provided for play by two persons having a game board, a plurality of numbered pieces, and rack members to hold the pieces so as to be readily visible to the respective players. The game board has a plurality of intersecting horizontally and vertically disposed rows of square spaces similar to a checker board. A plurality of consecutively numbered game pieces are provided which are placed according to the rules of the game on individual ones of the spaces in calculated order by the respective players. The pieces can be placed on the racks as drawn from a pile so as to be readily visible to each player, respectively, and providing a plurality of choices of the pieces prior to play upon the spaces in a manner as set forth in the rules of play. After covering all of the spaces with the pieces, the winner is determined by adding the respective sums of each vertical and horizontal row and the player with the highest bonus score determined by minimum deviation of his set of rows from a predetermined sum is the winner. It is seen that the game involves mental skill in applying a numbered piece to a given space, as for example, in a horizontal row so as to approach a predetermined sum without aiding the opponent in obtaining this sum in his vertical row to which the space is common.

Accordingly, an object of this invention is to provide a new and novel numerical game that is educational and challenging.

Another object of this invention is to provide a numerical game that is played by two persons in a test of relative skill.

Still another object of this invention is to provide a numerical game which is interesting to play and aids in teaching one rapid addition.

Still one other object of this invention is to provide a numerical game that is simple and easy to understand and provides a challenging battle of player skill.

A further object of this invention is to provide a game apparatus having a plurality of vertical and horizontal knited States Patent Patented Aug. 12, 1969 rows of spaces and an equal amount of numbered pieces placed in selected positions in the spaces to arrive at a predetermined numerical sum in each of the vertical .and horizontal rows, respectively, whereupon the player nearest to the predetermined numerical sum in most of the rows is declared the winner.

One further object of this invention is to provide a game apparatus that is economical to manufacture, simple to understand, and presents a challenging game that evaluates ones mathematical and thinking skill.

Various other objects, advantages and features of the invention will become apparent to those skilled in the art from the following discussion, taken in conjunction with the accompanying drawings in which:

FIG. 1 is a perspective view of the mathematical game of this invention illustrated as mounted upon a playing table in the normal position of play;

FIG. 2 is an enlarged top plan view of a game board and a sheet of numbered pieces of the mathematical game of this invention;

FIG. 3 is an enlarged plan view of the scoring portion of the game board of the mathematical game of this invention;

FIG. 4 is a top plan view of the game board and the separated numbered pieces of the mathematical game of this invention similar to FIG. 2 illustrating the same during an intermediate stage of game play; and

FIG. 5 is a top plan view similar to FIG. 4 illustrating a completed stage of the mathematical game of this invention.

The following is a discussion and description of preferred specific embodiments of the new mathematical game of this invention, such being made with reference to the drawings, whereon the same reference numerals are used to indicate the same or similar parts and/or structure. It is to be understood that such discussion and description is not to unduly limit the scope of the invention.

Referring to the drawings in detail, and particularly to FIG. 1, the mathematical game of this invention, indicated generally at 12, is shown on a conventional table 13 in the proper position of play. The mathematical game 12 is known as Double Cross and includes a large square game board 15, a sheet 17 of consecutively numbered game pieces 18, and a pair of rack members 20 used to hold the pieces 18 of each respective player.

As shown in FIG. 2, the game board 15 has an inner square playing section 21 comprised of a plurality of spaces 23 separated by strips 24. The playing section 21 has its corners adjacent mid-portions of sides 26 of the game board 15 thereby placing the diagonals thereof perpendicular to the sides 26. The spaces 23 are arranged in horizontally and vertically disposed rows 28 and 29, respectively, of seven each and identified by consecutive numerals 31 within triangular-shaped border sections 33. The numerals 31 are positioned so as to be readily readable by the opposed players to identify the horizontal and vertical rows 28 and 29, respectively, being played by the individual players. The name of the game Double Cross is placed in diagonally opposed corners of the game board 15 with the other corners having scoring tables 35 therein. As shown in FIG. 3, each table 35 has a. heading Scoring and a numerical total column and a credit or bonus points column. In this particular preferred embodiment of the invention, a mathematical total of 175 is considered a perfect score and given bonus points equal to a numerical total of 10 with deviations above or below this predetermined sum given a smaller number of bonus points until below or above 200 is given no credit. The application of the scoring table 35 in playing the game will become obvious.

The sheet 17 is perforated so as to be readily separable into the pieces 18 of equal size adaptable to individually cover a selected one of the spaces 23 during play of the mathematical game 12. The pieces 18 are numbered consecutively from 1 to 49 having the numerals thereon extended parallel to one diagonal of the square pieces 18 for reasons to be explained.

As shown in FIG. 1, the rack members 20 are of L shape in transverse cross-section and adapted to be placed in front of each respective player to hold the pieces 18 during play of the mathematical game 12. The rack members 20 are merely convenient tools to hold the pieces 18 so as to be visible only to the player using the same.

Additionally, the mathematical game 12 is supplied with a book or pamphlet entitled Double CrossRules of Play setting forth in detail the guide lines and steps of how to set up, score, and play the game. First, Double Cross is a game played by two persons having to deal with the placement of the forty-nine pieces 18 on the same number of spaces 23 on the game board 15. One player uses the vertical rows 29 and the other player the horizontal rows 28 with a total of the numbered pieces 18 in each individual row to approach the perfect or predetermined sum of 175. Therefore, the object of the game 12 is for each player by the end of play to make his rows individually add to 175 or as close as possible and, at the same time, try to prevent his opponents rows from adding up to the 175 total.

In the operation and play of the mathematical game 12, the numerical pieces 18 are placed face down on the table 13 and mixed up whereupon each player draws one of the pieces 18 and the highest numbered one plays first. The drawn numerical pieces 18 are placed back into the pile, again face down, mixed up, and then each player draws seven new pieces 18 and places them on his respective rack member 20.

The first player then starts off by placing one of his seven pieces 18 on the central one of the spaces 23 indicated generally at 38 (FIG. 2). This player then replaces the played piece 18 by drawing from the pile of pieces 18, and the second player thereupon places one of his seven original pieces 18 on a selected one of the spaces 23. This piece 18 played by the second player from his rack member 20 is then replaced by drawing from the pile as previously described for the first player and the players continue to alternate in this manner of play until all the pieces 18 are placed on the spaces 23. After the first play on the center space 38, the numbered pieces 18 may be placed on any of the spaces 23 but, once played thereon, -a piece cannot be moved. It is seen that the pieces 18 are placed on the game board so as to be facing in a common lateral direction relative to the players and, therefore, are readily visible to both.

In order to facilitate the play, upon placing the fourth, fifth, sixth or seventh numbered piece 18 in any of the rows 28 and 29, the player must announce the new total for that row. If the played piece 18 is the fourth, fifth, sixth or seventh one of the numbered pieces 18 in both of the two crossing rows 28 and 29, the player must now announce both of these new totals. Additionally, as soon as there are four pieces 18 in a given row 28 or 29 being played, the player keeps a running total of that row on a score pad or the like until it is filled. It is obvious that this procedure is necessary to eliminate the need for adding each row over and over before playing a piece 18 therein.

As shown in FIG. 4, during an intermediate stage of play, the players are facing each other with one playing the horizontal rows 28 and the other the vertical rows 29. As an example of the numerical sum announcement procedure, if the piece 18 numbered 13 is now played, the player announces 84 and 90 which indicates, first, the scoring of his respective vertical row 29 and, secondly, the opponents score in his horizontal row 28. It is seen that this is required as the piece 18 numbered 13 is the fourth one placed in the vertical row and the fifth one placed in the horizontal row.

On completing the game play as shown in FIG. 5, each player totals his respective rows 28 and 29 and converts his score to the bonus points as shown in the tables 35. For example, a player of the vertical rows 29 has scores of l83-202-143l76164-165-192, which, when converted to bonus points equals 4-0-0534-2, respec tively, for a grand total score of 18. Similarly, the other player has scores for the horizontal rows 28 of 193-190- 185170-171-15l165 for bonus points of 23-4 55- 14 for a grand total of 24. It is seen, therefore, that the horizontal row player has exhibited more skill in arriving at the largest grand total of bonus points and is declared the winner.

The average game played will normally consume 30 to 40 minutes and the score will range from 10 to 25 points depending on the relative score of the players with scores below and above this range indicative of poor and excellent play, respectively. It is obvious that the players engage in mental combat in attempting to arrive at the total of for each of the respective rows, while, at the same time, attempting to place the opponents rows at a sum as far removed from 175 as possible. Therefore, numerous combinations of plays are available requiring mental skill in foreseeing future plays in light of the pieces available to each player.

The game board of the invention has been illustrated with seven each of horizontal and vertical rows resulting in 49 spaces and pieces numbered consecutively from 1 to 49, inclusive. In this preferred embodiment, it is seen that the numerical total of the pieces is 1,225, exactly equal to 7 times 175 (the ideal score), whereby it is possible, however extremely unlikely, for a player to have all seven respective row scores equal to the predetermined ideal sum of 175.

Although the mathematical game is described for seven rows in the horizontal and vertical, the number of rows can be altered to change the degree of difliculty of the Double Cross game with the only major change being the determination of a new predetermined sum. This perfect average or sum can be readily determined by the following formula:

or, equally; wherein:

PS=perfect score N=number of horizontal or vertical rows It is seen that for a simpler six row game, the perfect sum would be:

and the pieces would be numbered from 13 6, to be placed according to the previously described Double Cross- Rules of Play on the corresponding 36 spaces.

As will be apparent from the foregoing description of the preferred embodiments of applicants mathematical game, a relatively simple and easy to understand game has been provided to test ones mental ability similar to the commonly known chess game.

While the invention has been described in connection with preferred specific embodiments thereof, it is to be understood that this description is intended to illustrate and not to limit the scope of the invention, which is defined by the following claims.

I claim:

1. An apparatus for playing a mathematical game requiring at least two players, comprising:

(a) a rectangular game board having a plurality of intersecting generally vertically and horizontally disposed rows of rectangular spaces, the rows being of equal number both vertically and horizontally, each space being common to one vertical row and one horizontal row,

square pieces beginning with numeral 1 and extending through the numeral which is the square of the number of vertical rows, each piece being the same (b) a plurality of consecutively numerically marked rectangular pieces beginning with numeral 1 and 5 extending through the numeral which is the square of the number of either vertical or horizontal rows, each piece selectively positionable within one of said spaces whereby the numerical sum of said pieces in each roW may equal a predetermined value and 10 any deviation therefrom may serve as an indication of relative player skill, said numerals on said pieces being positioned thereon so as to be upright when viewed along a diagonal of the piece, and

(c) the diagonals of said spaces extending perpendicu- 5 lar to respective sides of said game board so that size as each of the other pieces and selectively positionable within one of said spaces whereby the numerical sum of said pieces in each row may equal a predetermined sum and any deviation therefrom may serve as an indication of relative player skill,

(c) said numerals on said pieces being positioned thereon so as to be upright When viewed along a diagonal of a piece, and

(d) the diagonals of said spaces extending perpendicular to respective sides of the game board.

References Cited UNITED STATES PATENTS the indicia on said pieces are readily readable by 2,399,902 5 /1946 Wood both Playera 300,534 6/1884 Van Bibber. 2. A game apparatus as described in claim 1, wherein 1 457 333 1923 il said game board has scoring indicia on diagonally op- 1,633,445 6/1927 G il r a1, posed corners facing adjacent respective playing sides 2,170,909 8/1939 Moren, so as to be easily readable by the corresponding players. 2,871,581 2/1959 Guzak 273l35 X 3. An apparatus for playing a mathematical game requiring at least two players, comprising: FOREIGN PATENTS (a) a square game board having a plurality of inter- 174,228 1/1922 Great Britain, secting generally vertically and horizontally disposed 844,983 8/ 1960 Great Britain.

rows of square spaces of equal size, there being equal numbers of vertical and horizontal rows, each space being common to one vertical and one horizontal row,

(b) a plurality of consecutively numerically marked DELBERT B. LOWE, Primary Examiner US. Cl. X.R.

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