United States Patent 3744153

Arithmetic game with game board and board pieces bearing signs or indicia which represent the ciphers or digits zero to nine inclusive and calculation operators. The players are expected to do alternately as many arithmetical operations as possible with the arithmetical implements they dispose of. To determine the score obtained in each turn, the separate ciphers or digits used for composing one or more complete arithmetical results are added. In an attractive embodiment the game's implements are enclosed in a case.

Application Number:
Publication Date:
Filing Date:
Primary Class:
Other Classes:
273/282.1, 273/287, 434/191
International Classes:
A63F3/04; G09B19/02; (IPC1-7): G09B19/02
Field of Search:
35/31D,31F,35H 273
View Patent Images:
US Patent References:
3267590Educational game apparatus1966-08-23Browning
3077677Word and alphabet game device1963-02-19Malkin et al.
2811360Game apparatus1957-10-29Cohen
2320832Educational game1943-06-01Schoenberg et al.

Foreign References:
Primary Examiner:
Grieb, Wm H.
I claim

1. An arithmetic game comprising, in combination, a game board having thereon a playing field divided, by mutually perpendicular lines, into first rectangular spaces, aligned in mutually perpendicular first rows and first columns, for placing thereon first game pieces provided with digit symbols combinable with arithmetical operators and "equal" symbols to pose arithmetical equations; said playing field being further divided, by mutually perpendicular lines, into second rectangular spaces, aligned in mutually perpendicular second rows and second columns, for placing thereon second game pieces, some of which are provided with arithmetical operator symbols and others of which are provided with "equal" symbols; said first columns and rows alternating with said second columns and rows, respectively, whereby the four sides of each first space are bounded by two second rows and two second columns.

2. An arithmetic game, as claimed in claim 1, in which said arithmetical operator symbols and said "equal" symbols are imprinted in said second columns and second rows.

3. An arithmetic game, as claimed in claim 2, in which said arithmetical operator symbols are provided in alternate second columns and second rows, and said "equal" symbols are provided in second columns and second rows intermediate said alternate second columns and second rows.

4. An arithmetic game, as claimed in claim 1, in which said second spaces have a distinctive appearance distinguishing said second spaces from said first spaces.

5. An arithmetic game, as claimed in claim 4, in which said second spaces have dimensions differing from those of said first spaces.

6. An arithmetic game, as claimed in claim 4, in which said second spaces have a color differing from that of said first spaces.

7. An arithmetic game, as claimed in claim 1, in which each of said first game pieces is provided with a single digit symbol selected from the digits "0" through "9."

8. A game, as claimed in claim 1, wherein said game board is formed with recesses at each of said spaces, said recesses receiving said board pieces.

9. A game board, as claimed in claim 8, in which each of said recesses has a sloping bottom surface; said game pieces comprising blocks having correspondingly sloping bottom surfaces engageable with the bottom surfaces of said recesses.

10. A game, as claimed in claim 1, in which said pieces are blocks having a pair of opposite surfaces; said symbols being provided on only a single surface of a block.

11. A game comprising, in combination, a game board defining a playing field and constructed and arranged to receive board pieces at discrete spaced locations thereon; said game board carrying, between said locations, indicia imposing certain actions to be performed by the players; and a plurality of board pieces provided in multiples, for positioning at said discrete locations; said indicia representing arithmetical operators; at least some of said board pieces carrying indicia representing arithmetical elements useable with said operators; said game board being formed with recesses at each of said discrete spaced locations thereon, said recesses receiving said board pieces; and a two-part case releasably enclosing said game board and having a hand grip; the two parts of said case being substantially identical, and each part having, in longitudinal section, a substantially rectangular U-shape including a pair of elongated legs extending perpendicular to a base; said two parts being telescopable over said game board with said bases engaging opposite edges of said game board and the legs of each part overlapping legs of the other part; one leg of each part, adjacent its free edge, having projections from its inner surface engageable in openings adjacent the free edge of the overlapped leg of the other part; said projections extending through said openings into recesses in said game board.

This invention relates to a game comprising a game board defining a playing field, signs or indicia imposing certain actions to be performed by the players, a plurality of board pieces occuring in multiples, and some boxes for containing, in stock, well-ordered, a quantity of these pieces.

There are many commercially available board games of this type having for their object to offer the players sociability and relaxation. Besides these board games purely attuned to recreation, board games have come out during the last decades adding to the game, apart from a diversion element, also an educational element. With some games the votaries can either extend or improve their geographic knowledge, their linguistic skill or their general education. In other games, certain acts performed by grown-ups in daily life ex officio on the economical or international plane, are translated in such attractive, very simplified but nevertheless particular exciting form that, to broad strata of society, including both young and old persons, merely by practising such games, some insight is imparted with respect to matters which often, in reality, are very complicated.

It has appeared, however, that sofar game-composers have paid no attention to the domain of the normal art of arithmetics, or at least have by-passed the latently felt need for arithmetics as a game, although a game attuned to this art may be considered from an educational point of view as useful and as instructive as, for example, a game concerned with language teaching.

Broadly speaking, the invention has for its object to supply a hiatus obviously present in this domain by providing a game completely based on performing arithmetical operations and which is characterized by the fact that the signs or indicia on the board represent arithmetical operators and the pieces to be put on the board are constituted by arithmetical elements. The signs on the board prescribe a predetermined arithmetical operation and in this way they exert a certain compulsion on the players so that the number of freely possible operations with a given number of arithmetical elements is drastically limited. Now this requires the player to have insight in order to find, in spite of this small number of free possibilities, yet a solution yielding to him the highest possible score. The experience thus obtained by repeatedly playing the present arithmetic game, when doing arithmetical operations, and the ease thus obtained with which certain arithmetical operations are done by the votaries, are factors which could be of inestimable value in practical life, indeed, for certain professions, of decisive importance. In this manner the present arithmetic game can give parents and other educators an impression with respect to the question of whether or not their child is gifted particularly for arithmetics.

According to a further feature of the invention certain arithmetical elements are provided with ciphers or digits and other arithmetical elements bear designations of various arithmetical operators.

In a practical embodiment, the arithmetical elements are constituted as blocks bearing, for one thing, the ciphers or digits zero to nine inclusive, and for another thing the operators +, -, :, × and =.


1 board or playing-field divided into a plurality of

spaces, to which belong:

7 blocks bearing the cipher 0

8 blocks bearing the cipher 1

9 blocks bearing the cipher 2

9 blocks bearing the cipher 3

9 blocks bearing the cipher 4

9 blocks bearing the cipher 5

9 blocks bearing the cipher 6

9 blocks bearing the cipher 7

9 blocks bearing the cipher 8

9 blocks bearing the cipher 9

4 blocks blanks

20 blocks with the sign +

16 blocks with the sign -

15 blocks with the sign :

15 blocks with the sign ×

30 blocks with the sign =

2 boxes in which each player may arrange his blocks.

The intention of the game is to do arithmetical operations with the aid of the above enumerated calculation implements on the game board added thereto. To this end, each player has at his disposal a number of cipher or digits blocks and tries, each turn, to process as much as possible the cipher blocks he disposes of by combining them with suitable arithmetical operators into complete problems (inclusive of their solution), while putting the required pieces or blocks on the board. Each next problem to be composed with the aid of the blocks left at the player's disposal can only then be "written down" or laid out on the board if at least one of the terms or factors of the operations to be done is coupled to at least one of the terms or factors of an operation already "written down," it being necessary at the same time to take into account the signs or indicia present on the game board.

Although it is possible to play the game in a simplified form with a board scarcely provided with signs, the game's suspense can be intensified if, according to the invention, the board is divided by ruling the playing-field horizontally and vertically into lines and columns forming spaces, in which the arithmetical operators are located both in spaces of individual vertical columns and in spaces signs individual horizontal lines, whereas the = signs are located in spaces of other, likewise individual lines and columns, it being understood that between each "operator-space" and its adjacent "= -space," both in the vertical and in the horizontal sense, a free space is present for putting therein a number formed by cipher-pieces.

In this event the board is provided to its maximum with signs, so that the number of free operation possibilities is at a minimum and therefore the compulsion exerted the greatest. In this manner however the difficulty factor is also the greatest and playing the game under these circumstances will give the players the greatest satisfaction.

It is the intention to play the game with two persons though it has appeared that as much pleasure can be gained if it is played solo. This is possible when the solo-player every time he takes 10 cipher-blocks or during the game completes these to 10, puts these blocks such that the ciphers are not visible. If two players are playing together then, of course, they keep them a secret from each other. To this end the ciphers are provided at only one side of the blocks.

In order to let every player have as much as possible an equal number of ciphers, there is a total number of 91 cipher-blocks (inclusive of the blanks). Each player takes up to 10 cipher-blocks every time. Since it is in practise impossible to process the 10 cipher-blocks all in one turn, the players need not replenish their stock every time with 10 new cipher-blocks. On the average each player will process during each game 5 × 10 cipher-blocks.

So, it is in the interest of each player to process as many as possible of his cipher-blocks in each turn, on the one hand with a view to the number of points to be scored, on the other hand not to give his adversary player the possibility at the end of his turn to benefit from combination possibilities with ciphers or digits being left due to an incomplete processing of such possibilities.

Game tactics

The thrilling element of the game is not only the sensation experienced by the knowledge that the highest scores can be obtained by insight and correct composing of the ciphers or digits but also the suspense which is felt when watching an adversary player and weighing out the freshly emanating possibilities. Care should be taken that the ciphers are composed such that the second player gets the least possible chance to benefit from the results of the first player.

The above description is only a rather concise indication of all possibilities which, the game incorporates and which when the game is played with full affection and enthusiasm, lead to a great diversity of results. The direct practical usefulness is that one can handle ciphers much faster and make oneself familiar with the art of quick and instant calculations in a playful and pleasant way.


The invention will now be described with reference to the figures of the attached drawing in which an embodiment of the game board has been illustrated.

FIG. 1 shows the playing-field of the arithmetic game according to the invention;

FIG. 2 shows an embodiment of the game board provided with recesses for receiving the playing-pieces, which game board is enclosed in a kind of cross-section case;

FIG. 3 shows a portion of a cross-section of a game board of FIG. 2 taken along the line III--III in FIG. 2; and

FIG. 4 shows the case in which the arithmetic game according to the invention has been accommodated.


In FIG. 1 the playing-field is divided by horizontal and vertical ruling 1 and 2 into a plurality of lines and columns, each sub-divided into spaces 3-6. The even lines and the even columns are provided with signs in such a manner that the pure operator signs figure in the second, sixth etc. line or column, and the = signs in the fourth, eighth etc. line or column. These signs occur exclusively in the odd spaces 3 and 4, respectively, of the lines or columns mentioned. In this way there are still spaces 5 and 6 left between the spaces just mentioned, of which the spaces 6 have no function in the game. The spaces 5 on the contrary, lying between each "operator-space" 3 and its adjacent "=space" 4, both the vertical and the horizontal sense, serve for receiving a number to be formed by the cipher or digit pieces.

The game is played as follows:

The blocks with ciphers or digits zero to nine inclusive come unexposed on the table, together with five blanks. The remaining blocks are kept invisible at a separate place (while being described on both sides).

Each player takes one of the ciphers to determine the first player; low starting. First, the ciphers just drawn are added, unexposed, again to the other ciphers and all pieces are now shuffled well. Each player takes then 10 blocks putting them, visible for himself, in front of him. The easiest way to play is to sort out the ciphers from zero to nine inclusive. The player who has drawn the lowest cipher now starts the game by doing any kind of arithmetical operation and, being the first player, he is free ot make a choice between the four possibilities of adding, subtracting, multiplying, or dividing.

Therefor he uses the hatched space 3A (see centre of the playing-field) by placing thereon the operator-block of his choice. If it is possible to make, out of the arithmetic material the player disposes of in a playing turn, for instance the calculation 32 × 3 = 96, then he puts the ciphers, which he has taken out of the 10 cipher-blocks chosen, in such a manner on the board that the ciphers 32, 3 and 96 come into the spaces 5A, B and C respectively. The × and + sign are taken free out of the signs placed separately and are put in the spaces 3A and 4A respectively. Herewith the first sum is finished. Now the ciphers used in this calculation are counted, viz. 3 & 2 & 3 & 9 & 6 is 23 points. So the first player starts with a score of 23 points which are noted adjacent his name. It goes without saying that there are still ciphers left, and so the first player continues trying to do other arithmetical operations whereby he has now to respect the signs indicated on the game board. He may then play, for instance, as follows by placing below the number 96, already occuring, a + sign (see space 4B on the game board), thereafter the ciphers 3 in space 5D and next on, after placing an = sign in the space 4B, two 9's in space 5E. He benefits then from the result of the sum made in first instance and counts now as follows 9 & 6 & 3 & 9 & 9 makes 36, which number is added to the number 23 already scored. He goes on doing one or more arithmetical operations if possible, and adds every time the total of the ciphers of the result thus composed to the results of additions of operations already previously composed.

If at the end he has still one, two or even three ciphers, and sees no possibility to do another operation, then he finishes his playing-turn by replenishing his ciphers or digits up to 10 pieces.

Now the second player starts doing arithmetical operations, and it goes without saying that he will try to benefit as much as possible from the operations already existing. He is, however, obliged to follow the indications represented by the signs as indicated on the game-field.

If the player disposes of a "blank" among the 10 various ciphers, he can use it for any cipher desired. Example: A player has the possibility to make a sum with the term 97 already appearing on the board. He has a 2 and can make 97 + 2 = 99. But he only disposes of one 9 and by using now a blank, he obtains 97 + 2 = 9 & blank. The blank counts in this case for a 9. The score so obtained is now 9 & 7 & 2 & 9 & 9 is 36. In continuing the game, the player can only proceed with the real cipher 9. The blank has only once the allotted value.

It goes without saying that the blanks have to be used carefully since they may be of great value to their owner and have no value for the adversary player. If a player disposes of two blanks, which is possible, he is only permitted to use one in each sum. The result of a sum must always indicate at least one real cipher. So a blank can at any time assume the value of one of the ciphers zero to nine inclusive. Example: 97 & blank = 99 is of course also permitted. The blank has been allotted here the value of 2.

If each of the players has still left, at the end of the game, ciphers or digits which cannot be converted into sums, then the total thereof is subtracted from the overall score. He who has gained the highest score is winner of the game.

The following remarks should be carefully considred:

The numbers should be composed of no more than two ciphers; or digits in this way the highest number can only be the number 99.

Each player should carefully observe what he leaves for a next player. So he will have to try for himself to benefit as much as possible from the higher ciphers and try to leave the lowest possible ciphers to his adversary player.

Coupling to existing operations or making a connection therewith from all sides is allowed. So it is possible at a given moment that two operations result in one turn. The total of the ciphers of each requires is counted and noted.

It can soon be ascertained that it requires some mental activity and that surprising results are possible provided the player knows how to combine and sees the many, many possibilities.

The player is obliged to follow at any time the instructions given by the signs on the playing-field.

The game-board can be made of card board on which the operator signs are printed as represented in FIG. 1. For the cipher pieces, use is made of blocks made of wood, plastic or similar material which blocks are put on the relevant spaces 5. In a practical embodiment, the spaces 5 are constituted as recesses or depressions. In the latter case the game-board 7 can be manufactured from a sheet of plastic material, in which the depressions 5 are provided by means of a suitable die. A game-board thus manufactured is represented in FIG. 2. It will be appreciated that the board-pieces now can slide no longer by unintentional pushing against the board.

In FIG. 3, a portion of a cross- section along the line III--III in FIG. 2 is shown. It is to be noted, that the depressions 5 in the sheet-like game-board 7 have an inclined bottom 8 in which cipher-blocks 10, likewise provided with an inclined under-face 9, can be fitted such that their upper-face 11 projects a little beyond the edges 12 surrounding the spaces 5. In spite of their relatively rigid position in these depressions 5, the blocks 10 can easily be moved out of the nests or depressions 5 due to the inclined faces 8 and 9, which measure does not aim at removing the blocks from the spaces at the end of the game but rather during the game when a player has made a mistake and has put the wrong block or when he wants to correct his "move" anyway. Instead of wedging, inclined faces 8 and 9, the bottom 8 of the depression 5 can be given the shape of a pit and the under-face 9 of the cipher-blocks 10 a curved plane, f.i. part of a cylinder or of a sphere.

The invention provides further a receptacle in the shape of a case for storing the game-board and the pieces at the end of the game, or for temporary storing when the game is not yet finished but has to be interrupted anyway. The case consists in essence of two case halves each constituting a U-shaped flap 13 and 14 resp. as represented in FIG. 2. These flaps are slid from both sides over the game-board 7 join each other near the centre area. The free ends 15 and 16 respectively of the flap 13 are provided with a number of burls 17 and apertures 18 respectively cooperating with apertures 19 and burls 20 respectively on the free ends 21 and 22 resp. of the flap 14. In this way the free edges of both flaps 13 and 14 can be joined with little overlap by means of the burls and apertures, whereby the burls 17 penetrate into the spaces 5a and the burls 20 reach below the edge 12a. Between the edge 12b and the side-edge 12c there is a reservoir 23 for storing the playing-pieces which reservoir is limited fore and aft by part of side-edges 24a and b (FIG. 4), lying perpendicular to the side-edges 12c and 12d of the game-board 7. During the game the flaps 13, 14 can, if desired, be arranged vertically on their back 25, 26 in front of the pieces of each of the players so that they cannot crib from each other.

In FIG. 4 the game-board is represented complete as a portable unit, viz. as a case model in which the flaps 13 and 14 partly overlap. In the front side-edge 24a a grip 28 is mounted with the aid of securing means 27 for conveniently carrying the case.