US2215544A - Machine to play game of nim - Google Patents

Description

Sept. 24, 1940. E. u. CONDON ET AL 2,215,544

' MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet l WITNESSES? 1 INVENTORS fawo/a dl'molgiamkLfiwnq,

. M I BY 11 Sheets-Sheet 2 E. U. CONDON ET AL MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 Sept; 24, 1940.

WITNESSES: %W @Z Sept. 24, 1940. E. u. CONDON- ET AL MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet 3 INVENTORS [dim/1M Candw; fem/d1. 701 040,

WITNESSES J I I,

Sept. 24, 1940.

E. u. CONDON El" AL 2,215,544

MACHINE TO PLAY GAME OF N'IM Original Filed April 26, 1940 ll Sheets-Sheet 4 ATTORNE p 24.1940. E. u. CONDON ET AL. 2,215,544

MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet 5 I N V E N TO RS [dry/#0600104 er ATTORN 11 Sheets-Sheet 6 TO PLAY GAME OF NIM E. u. CONDON ET .51.

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Sept; 24; 1940. E. u. CONDON ET AL 2,215,544

MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 11 Sheets-Sheet '7 ATTORNEY Sept. 24, 1940. E. u. CONDON E1 AL 2,215,544

MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet 8 ATTORNE Sept. 24; 1940, I E. u. CONDON ET AL MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet 9 WITNESSES:

Sept, 24 194() E. U. CONDON ET AL MACHiNE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet l0 I Sept. 24, 1940. E CONDQN AL 2,215,544

MACHINE TO PLAY GAME OF NIM Original Filed April 26, 1940 ll Sheets-Sheet 11 ATTORNE Patented Sept. 24, 1940 momma 'ro PLAY GAME or NIM.

Edward U. Condon, Edgewood, and Gereld L. Tawney and Willard A. Derr, Wilkinsburg, Pa., assignors to Westinghouse Electric & Manufacturing Company, East Pittsburgh, Pa., a corporation of Pennsylvania- Application April 26, 1940, Serial No. 331,784

17 Claims.

Our invention relates to control apparatus and has particular relation to electrical apparatus for automatically making the moves of one party in a game between two opponents.

Nim is played by two opponents with a plurality of sets of like elements. There may be any arbitrary number of elements in each set but it is preferred that no two sets shall have the same number.

The players make their moves alter-1 the game.

Nim is to a certain extent similar to checkers. The latter game can be won or lost during the first few moves. Unless the elements are initially arranged in a winning combination, Nim can be won by the player making the first move. Mathematical analysis reveals that to win at Nim, a player must first express the number of elements in each set as a sum of diflerent integral or zero powers of 2. He must then establish and maintain an array of sets such that allintegral or zero powers of 2 contained in the numbers of elements of the sets are present in an even number of sets. The number of elements removed by the other player in his turn from one set contain either one power of 2 or several different powers of 2, and therefore, there remain one or more powers of 2 in an odd number of'sets after the latter moves.

The second player cannot therefore establish a winning combination once it has been established by his opponent and the latter can always reestablish the winning combination.

For a better understanding or Nim and. the manner in which it is played, we may consider an example.

Assume that originally there are three sets of like elements; 9 elements in set No. 1; 7 elements in set No.12, and 5 elements in set No. 3. In playing the game, each player, in his turn, may remove any number of elements from set No. 1, set No. 2, or set No. 3.

example, remove 6 elements from set No. 1 in making his first play and after the other player moves, he may remove any number of elements He may, for

from the same or another set, say set No. 3. The

player removing the last element is the winnereven number oi sets.

Initiall the array of sets may be analyzed as follows:

The zero power of 2 is present in all three sets. The first power of 2 is present only in set No. 2. The second power of 2 is present in set No. 2 and set No. 3. The third power 01' 2 is present in set 10 No. 1. The first player can assure himself of winning the game by removing sufl'lcient elements from set No. l to balance the odd 2 in set No. 2. Accordingly, he removes 7 elementsfrom set No.

1, leaving two elements. Set No. 1 now contains only the first power of 2; set No. 2 contains the second power of 2,-the first power of 2 and the zero power of 2; and set No. 3 contains the second power of 2 and the zero power of 2. It is seen that each power of 2 contained in the sets is present in two sets. After the first player has made the play just suggested, the second player cannot win the game regardless of what play he makes unless the first player fails to maintain the winning combination.

For example, if the second player removes one element from set No. 2, leaving six elements in this set,'the first player should remove one element from set No. 3, leaving the combination set No. 1 two elements, set No. 2 six elements, and set No. 8 four elements. If the second player now removes another element from set No. 2, the first player should remove one element from set No. 1, leaving set No. 1 one element, set No. 2 five elements, and set No. 3 four elements. If the second player now removes another element from set No. 2 the first player removes the remaining element from set No. l leaving set No. 2 four elements and set No. 3 four elements. If the second player now removes an element from set No. 3, the first player removes an element from set No. 2, leaving 3 elements in each of the two sets. If the second player now removes still another element from set No. 3, the first player removes an element from set No. 2 and on the removal of a further element by the second player from set ture shown in Fig. 1;

an electrical system which shall perform the plays of one player in the game of Nim.

A further object of, our invention is to provide electrical apparatus for playing Nim wherein the initial array of elements shall be such that the player opposing the apparatus shall be capable of winning if he makes a series of correct moves.

More concisely stated, it is an object of our invention to provide a device for playing Nim and for displaying the arrays and moves while the game is being played.

In accordance with our invention, we provide a system in which the like elements used in playing Nim are a plurality ofsets of lamps. Any combination of sets may be established by extinguishing certain of the lamps in each of the sets. The lamps are connected in circuits which are controlled by manually operable switches. A player may in his turn extinguish any desired number of lamps in any one set only by operating a switch. Thereafter he may operate another switch, causing certain additional lamps in one of the sets to be extinguished automatically. The operations may be repeated by the player until either heor the machine extinguishes the last lamps. Preferably the number of lamps initially energized is such that the player who operates the control element may win, if, in his first move, he establishes a winning combination and if he maintains the winning combination when making the following moves in his turn. However, if the player makes one incorrect move, the machine sets up the winning combination and thereafter the player is certain to lose.

The novel features that we consider characteristic of our invention are set forth with particularity in the appended claims. The invention-itself, however, both as to its organization and its method of operation, together with additional objects and advantages thereof, will best be understood from the following description of a specific embodiment when read in connection with the accompanying drawings in which:

' Figure lie 9. view in perspective oi. a structure in accordance with our invention;

Fig. 2 is aview in side elevation of the struc- Fig. 3 is a view in rear elevation of the structure shown in Fig. 1 with the cover removed in part; and

Figs. 4 to 12, together, constitute a diagrammatic view showing the electrical circuit used in the practice of our invention.

Tm: MECHANICAL STRUCTURE The apparatus shown in the drawings comprises a casing l3 having the form of a desk.

The casing comprises a vertical chamber I5 from the front surface of which communicating chamber l'l extends. The latter chamber has a height somewhat greater than half the height of the chamber IS. The top IQ of the chamber i1 is at a slight angle to the-horizontal and constitutes a platform similar to the working surface of a desk. In the surface 2| of the chamber l5, above the top is, a plurality of lenses 23 are arranged in vertical rows. Behind each row the lamps used in the playing of Nim are mounted.

Specifically our invention is shown as applied in a system in which there are four sets of elements and a maximum of seven elements in any .set. There are accordingly four rows of lamps with seven lamps in each row. The rows are designated, respectively, as a, b, c and d, and the individual lamps in each row are identified by the letter of their row and a number, depending on their position with reference to the top of the row. Thus the lamps in row a are al, a2, a3, a4, a5, a8 and a! from top to bottom; the lamps in row I) from top to bottom are bl to N; the lamps in rowc from top to bottom are cl to c1; and the lamps in row d from top to bottom are dl to (11.

The surface ll of the chamber I5 is also provided with short slots 25, 21 and 28 behind which counters 3B are disposed. The counter on the extreme right PWC indicates the number of games won by the player, the counter in the center MWC indicates the number of games won by the apparatusa'nd the counter on the extreme left TP indicates the total number of games played.

Just above the platform is, the surface 2| of the chamber I5 is provided with an opening 3! partially enclosed'in its lower end by a semicup 33 into which a token drops when a player Wins a game. The tokens are stacked in a channel 35 extending at a slight angle to the vertical from the top of the chamber I5 to the opening 3| and are released one at a time when a relay SG is actuated anda actuates the token release device TRL.

Near the top of the surface 2| there is an elonratus is disposed. A cube 39 is supported from the top of the chamber I! on legs ll. In each of the vertical faces of the cube 4, rows of lamps 43 are disposed. The lamps in each of the rows in the faces of the cube are connected in parallel with correspondingly positioned lamps. The cube 39, therefore, displays in all directions and at all times the same pattern as the lamps in the rows a, b, c and d behind the lenses 2!. The lamps behind the lenses are used in playing Nim with the apparatus, and the lamps on the cube indicate the progress of the same as it is being played. I

A plurality of relays for performing the various operations in playing the game are disposed on a frame 45 in the chamber 15. The relaysand the lamps may be energized from theusual commeroial alternating current supply through a plurality of power supply units, each consisting of a transformer (not shown) and a dry rectifier 41. The power supply units are disposed in the shorter chamber l1 below the platform ll.

From the top of the chamber 1! a. pair of lamps P and M extend. The lamp P is green and is energized when the player is making a move. The

The circuit The lamps a! to al, bl to D1, cl to 01, and dl to d! used in playing the game are connected in circuits which are controlled by relays Al to A7, Bl to B1, CI to C1 and D! to D1, respec-- tively. The relays are provided with back contacts lAl-to 1A7, 1131 to I31, iCl to I01, and ID! to ID! which normally maintain the lamp cir-v cuits closed. The relays Al to A1 are controlled by a master relay A, the relays Bl to B! by a master relay B, the relays Cl to C1 by a master relay C, and the relays DI to D! by a. master relay D. The master relays are actuated by.

pushbuttonsPA, PB, PC and PD, respectively,

which are disposed in a row in the platform I9 so as to be conveniently operated by a player. When a player operates one of the pushbuttons PA to PD, he extinguishes the energized lamp having the lowest subscript in the corresponding row. Successive operations of the same pushbutton extinguish other lamps in the same row in succession. Once a player has actuated a pushbutton in any row, the pushbuttons corresponding to the other rows are locked out by the operation of relays AL, BL, CL and DL, respectively. The player may, however, actuate another pushbutton M'IR which energizes a relay TR so that the apparatus operates automatically to extinguish lamps in one of the rows, thus preparing the apparatus for another play by the player.

At the beginning of the game not all of the lampsin all of the rows are energized. Certain of the relays AI to D1 are initially actuated so that a selected combination is displayed. The apparatus may be designed so that any number of the combinations that can be made with four groups of seven elements each can be displayed. However, space limitations do not permit the use of all of the combinations, and, therefore, in the practice of our invention only a selected number of combinations are used. In the apparatus shown in the drawings, the combinations set forth in the following table are displayed in sequence.

The sequential display of the combinations is controlled by the relays SI I, SI2, S2I, S22, S3I, S32, SM, S42, S5I, S52,-S6I, S62, SII, S72, S8l, S82, and SSH, S92. The combinations are permutated by the operation of relays N, P and Q.

The performance of the apparatus is de pendent on the automatic analysis of the number of the energized lamps in each row into sums of zero or integral powers of 2. Since the maximum number of lamps" that may be energized in any row is 7, the only powers of 2 to be considered are the zero power, the first power, and the second power. The relays AZ, BZ, CZ and DZ are actuated when the numbers of energized lamps in the corresponding rows (1., b, c and d, respectively,

contain a zero power of 2; the relays AF,BF, CF

and DF are actuated when the numbers of ener gized lamps in the rows a, b, c and (1', respectively contain a first power of 2; and the relays AS, BS, CD and DS are actuated when the numbers of energized lamps in the rows a, b, c and d, respectively, contain a second power of 2. To properly play the game, the apparatus must also determine whether any power of 2 is, contained in the number of energized lamps in an even number or an odd number of rows. For this purpose, the relays EZ, EF' and ES are provided. These relays are energized if the zero power, the first power and the second power, respectively, are contained in the number of energized lamps in an even number of rows. The relays are also energized if the corresponding power is entirely absent from the number of lamps in all of the rows.

When the transfer button MTR is actuated and actuates the relay TR, the apparatus may operate in two different ways. If all of the powers of 2 contained in the numbers of lamps in the rows are present in an even number of rows, the machine performs a random operation. In such a case the relay RM is actuated and then the relay RMS is actuated. This is followed by the actuation of one of the relays AR, BR, CR, DR, which selects the row of lamps a, b, c or d, respectively, in which the number of energized lamps is a maximum. A certain number of the lamps in the selected row is then extinguished by the cooperation of the relays RI, R2 and R3, the

relays X, Y and Z, the relays RX and RY, and the relays RCI, RC2 and RC3. The number of lamps which'is extinguished is determined by the sequential operation of the relays RI, R2 and R3, relay RI being actuated when the apparatus makes the first random move; R2 being actuated 20 when the apparatus makes the second successive random move, and R3 being actuated when the apparatus makes the third successive random move. RI deenergizes one lamp, R2 two and R3 three. If further successive random moves are 25 required, the sequence is repeated.

If the powers of 2 contained in the numbers of lamps in the different rows are not present in an even number of rows when button MTR is operated, cooperation of the transfer relay TR with 30 the relays EZ, EF, ES results in actuation of the .relays CM and CMS. In such a case the player has manifestly made an incorrect movev and the relays CM and CMS now produce a sequence which results in a correct move so that after one incorrect move by the player, the apparatus is assured of winning the game. In such a case,

the correct row is selected by the cooperation of relays CM and CMS and relays AZ, AF, AS, BZ, BF, BS, CZ, CF, CS, DZ, DF, DS, which in turn control relays ARZ, BRZ, CRZ and DRZ, AR, BR, CR and DR, which correspond to the lamps a, b, c and (1, respectively.

The transfer operation is controlled by relay TR and relay TH! which are actuated when relay T9 is actuated. Relays TI to T9 are actuated subsequentially after the transfer relay TR is energized. The former relays control the red lamp M. The lamp M is energized-when the transfer operation begins and is gradually deenergized until the transfer operation is completed. The relay Tlll cooperates with the interlocked relays PI and P2 which initiate the actual extinction of lamps. After the game is completed, the resetting for a new game takes place by the operation of the relay RE. Relay ER deenergizes transfer relay TR when the relay RM is set for a random operation involving the extinguishing of more energized lamps than are available. For example, if only one lamp in each row is energized and relay RM is set to extinguish three lamps, relay ER deenergizes relay TR. As indicated, relays CMS, RMS, TI to T9, PI, P2 and P3 are slow to release but pick up instantaneously.

Player makes first move To illustrate the operation of the apparatus, we shall trace the performance of the machine when a game is being played therewith. When the power supply switch (not shown) for the apparatus is closed, all of the lamps al to dl are energized. In addition, relays AS, BS, CS and DS are energized. Relay AS is energized through contact 2A4 and conductor 5|, relay BS is energized through contact 2B4 and conductor 53, re- 7 lay CS is energized through contact 2C4 and conductor 55, and relay DS is energized through contact 2D4 and conductor 51. Because relays AS to DS are energized, relay ES is energized. The

BI, actuating the relay, opening contact IBI and extinguishing lamp bl. through contact SBI.

Contact lSI 2 closes a circuit extending through The relay is locked in conductor 69, conductor I I, conductor I3, relay CI, extinguishing lamp cl. In an analogous manner, contacts 6SI2, SSH and 4S|2 extinguish lamps c2, c3 and c4. Contacts 3SI2, 2SI2 and I SI 2 extinguish lamps ill to :13, respectively. The display of lamps then corresponds to combination I on the chart. There are seven energized lamps in row a, six energized in row I), three energized in row 0, and four energized in row (1.-

Relay N is, moreover, actuated through contact 2P, conductor 15, contact ISII and relay SI I.

Relays AZ and AF are now actuated in addition to AS. Relay AZ is energized through contact IAN and conductor 11. Relay AF is energized through contacts 2Al and conductor IS. Relay BF is energized through contact 232 and conductor 8|. Relay CS is now deenergized because contact 204 is open. Relay CF is energized through front contact 2C4, contact 206, and conductor 83. Relay CZ is energized through contact ICN and conductor 85.

Player moves With the apparatus in the condition just described, the player elects to omrate button PA. Relay A is now actuated in a circuit extending from the back contact IRMS, contact ICMS, conductor Bl,- back contact 2DL, back contact 30L, back contact 2BL, conductor 89, pushbutton PA, conductor 9i, relay A. Relay AI is now actuated through contacts 4A2, 4A4, 4A6, LAN and 2A and lamp aI is extinguished, Relay AL is also actuated in a circuit extending from positive condoctor 89, through contact IA and conductor 93. Relay AL locks out the other rows of lamps b,-c and d and prevents the player from extinguishing lamps in the other rows, since by the rules of the game he is permitted to extinguish the lamps in only one row in making a play. When key PA is released, relay A is deenergized and relay AN is' energized in a circuit extending through contact 3A, contacts 5AI, 5A2 and conductor 95. AZ is then deenergized because contact IAN is opened. AZ is deenergized now to denote that the row contains no zero power.

Since the number of zero powers of 2 which are now contained in the numbers of energized lamps in the difierent rows is odd, the relay E2. is deenergized. This relay was originally energized in a circuit extending through front con tact EAZ, back contact 232, front contact 2G2, and back contact EDZ. Since front contact 2A.! is opened, relay EZ is now deenergized.

One keying operation is now completed. The player could elect to stop his play at this point but he continues and operates key PA again. In this case, relay A is again actuated and this time relay A2 is actuated through contact 2A, front contact ZAN, back contact 4A1, back contact 4A5, back contact 3A3, and contact 4AI. Lamp a2 is, therefore, extinguished. Moreover, relay AF, which was originally maintained actuated through the back contact 2A2, is now deenergized since this contact is opened. There is, moreover, now an even number of rows, the energized number 01' lamps of which contain a first power of 2, and, therefore, relay EF is actuated. This relay is actuated in a circuit extending through back contact 3AF, front contact 4BR, front contact 36F, and back contact BDF- When the player new releases button PA, relay A is deenergized and relay AN is deenergized because contact 5A2 is open. Relay AZ is now energized because contact IAN is closed and relay EZ is energized because front contact ZAZ is again closed.

The'player now elects to again press button PA. This time relays A and A3 are energized in succession and-lamp a3 is extinguished. When the button PA is released, relay A is deenergized and relay AN is energized through back contact 3A; contact 4A3, and contact 5A4. Relays AZ and EZ are then deenergized in succession.

The player now again actuates button PA. Thus time relays A and A4 are actuated in succession and lamp a4 is extinguished. Now relay AS is deenergized because back contact 2A4 is opened, and because front contact 2A4 is closed relay AF is energized through contact 2A5, contact 2A6, and conductor 19. The operation of relays AS and AF is in accordance with the condition of lamps (1. There are now only 3 a lamps energized and, therefore, there is no longer a second power contained in the number of energized a lamps, but there isa first power. Next, relay ES is energized because the number of rows of lamps in which the second power of 2 is included in thenumber of energized lamps is even. The circuit for relay ES extends through back contact 3AS, front contact 438, back contact 30S and front contact 3DS. Moreover, relay EF-is deenergized because front contact 3AF is opened. When the button PA is now released, relays A and AN are successively deenergized and in succession relays AZ and EZ are energized.

n The player again operates button PA. This time relays A and A5 operate, lamp a5 is extinguished, and on the release of the button, relay A is deenergized, relay AN energized and relays AZ and 'EZ are deenergized in succession.

A further operation of the button PA results in the sequence of operations, actuation of relays A and A8, extinction of lamp a6, deenergizetion of relay AF, energization of relay EF', release of button, deenergization of relays A and AN, energlzation, of relay AZ and relay EZ. The player has now elected to have the extinguishing of the above mentioned lamps constitute his move. He hasextinguished six lamps so that only one lamp remains energized in row a; The

number of lamps are now as follows:

How a 1: 2 Row 1) 6=2 +2 Row c 3: 2 4-2 Row d i=2 number of rows, the piayer has made a correct 1 move. Ihe relays which are now energized to indicate the powers of 2 which are present in the various rows are AZ, BF, BS, EN, CA, CF, DS, EZ, EF and ES.

Apparatus makes a play The player now operates the transfer. key MTR. The operation of the key closes a circuit through relayTR extending through back contact IRMS, contact ICMS, conductor 81, back contact IBL, front contact 3AL, conductor 91, button MTR and conductor 99. Relay TI is now energized through contact 2TR, conductor IOI, and back contact ITI'II. Following relay TI, relays T2 to T9 are energized in succession, rel'ay T2 being energized through contact ITI, relay T3 being energized through contact IT2, etc. A negligible length of time elapses before relay T9 is energized. As relays TI to T9 are energized, the resistances I03 in series with the lamp M are successively short circuited.

The actuation of relay TR also produces actuation of relay RM which is the relay for causing the apparatus to make a random play. The relay RM is actuated in a circuit extending through contact 2TR, conductor IDI, front contact 21328, front contact 2EF, front contact 2EZ and contact 2CMS. Relay BR is also actuated on the actuation of relay TR. The circuit for relay BR extends through contact ITR, conductor I05, back contact IDR, back contact ICR, back contact IBR, back contact. IAR, conductor I01, front contacts IES, IEF and IEZ, conductor I09, back contact 2AS, front contact 2BS and conductor Relay RMS is energized through contact 2RM of relay RM. Relay RI is energized in a circuit through contact 3RMS, conductor H3, and back deenergized and contact ITI opens after a short time delay. The opening of contact ITI is followed by. the opening of contacts -IT2 to |T8 and the gradual deenergization of relays T2 to T9. Lamp M is, therefore, gradually dimmed.

The release of T9 completes a circuit for energizing relay PI. The circuit for relay PI extends through contact 2TR, conductor IIJI, front contact ITIII, back contact IT9, conductor I I1, and back contact 3Pa. Actuation of PI is followed by actuation of P2 through front contact 2PI. The circuit through relay PI is now opened because back contact 3P2 is opened. However, contact 2PI remains actuated. Therefore, relay B is actuated. This relay is in a circuit extending through contact 2TR, conductor IOI, front contact ITIII, back contact IT9, conductor In, front contact 3P2, contact IPI, conductor H9, contact IRM, conductor I2I, contact 3BR, conductor I23, contact IBS, conductor I25 and conductor I2'I. Relay B2 is, therefore, energized in a circuit extending through contact 2B, front contact 2BN, back contact 4B1, back contact 4135, back contact 3B3, and contact lBI. Lamp D2 is, therefore, extinguished and relay BF is deenergized because back contact 232 is opened. Since the number of rows with a first power of 2 is now odd, relay EF opens.

After contact IPI of relay PI opens, relay B is deenergized. Relay RCI is now closed in a circuit extending through back contact 2PI, contact 2P2, conductor I29, contact 5RM, conductor I3I, back contact IRY and back contact IRX. Moreover, relay P2 is deenergized because front contact 2PI is opened but the contacts of relay P2 are not actuated for a short interval of time.

Because front contact 3B is now open, the circuit for relay BN is opened and this relay is deenergized. By the actuation of relay RCI the holding circuit of relay RM is opened at contact 3RC I. The holding circuit extends through contact IRE, conductor I33, contact 3RCI, conductor I35, contact 3RI, conductor I31 and contact 3RM. Because contact IBN is closed, relay BZ is actuated. Because contact 2RM opens relay RMS is deenergized and after a predetermined delay, its contacts open. Because contact 4RM is opened, transfer relay TR is deenergized.

Sufficient time has now elapsed so that the contacts of relay P2 drop out. Moreover, because front contact 2BZ closes, relay EZ becomes deenergized, as is necessary, since the zero power of 2 is now present in an odd number of rows. Relay RMS has not as yet dropped out and RX is energized through front contact IRMS, conductor I39, contact 2RY, contact IRCI and relay RCI. Because contact 2TR is opened, the holding circuit for relay TIfl through front contact ITIO is opened and TH] is deenergized. Relay BR is deenergized because contact ITR is opened. Since front contact 2TH) is opened and back contact 2TIO is closed, lamp M is extinguished and lamp P is energized.

Sufficient time has now elapsed so that the contacts of relay RMS drop out. Because front contact IRMS opens, relay RX drops out and relay RCI, which was sealed in through front contact IRMS, also drops out. The random move of the apparatus is now at an end and the following relays are now energized: AZ, BZ, BS, CZ, CF, DS, ES, X and RI.

Player makes second move lamp c5 and relay CL locks out the other pushbuttons PA, PB and PD. When button PC is released, relay C is deenergized, relay CN energized, relay CZ deenergized, and relay EZ energized. Another operation of button PC produces the sequence: C energized, C6 energized, lamp c6 deenergized, relay CF deenergized, and relay EF energized. On the release of button PC, relay C. is deenergized, relay CN deenergized, relay CZ energized and relay EZ deenergized. Another operation of button PC causes relay C to be energized, relay C1 to be energized and, lamp c! to be deenergized. The release of button PC causes relay C to be deenergized, relay CN to be energized, relay CZ to be deenergized and relay ROW a 1: Row D 5:2 +2" Row c 0:

There are an even number of rows containing GED made a correct move, and when the apparatus moves, it is again to make a random move. The following relays are energized: AZ, 132, ES, DS, C L, EZ, ES, EF, RI, X.

Apparatus makes a second random move The player new again operates the transfer button MTR. Relay TR is energized in the same manner as before, as are relays TI and RM. Relay BR is energized in a circuit extending through contact ITR, conductor I05, back contact IDR, back contact ICR, back contact IBR, back contact IAR, conductor I07, front contact IES, front contact IEF, front contact IEZ, conductor I09, back contact 2A8, front contact ZBS and conductor ill. Following the actuation of relay TI, relays T2 to TIII are sequentially energized. Relay RMS is energized through contact ZRM. Because contact 3RMS is closed, relay R2 is energized in a circuit through contact SRMS, conductor H3, back contact i Z, back contact IY, front contact EX, and contact ZRI. Relay CL is deenergized because. back contact IRMS is opened. When relay TlD is energized, lamp P is deenergized and lamp M is energized through front contact 2'150. Relays Ti to T9 are next sequentially deenergized with a predetermined delay and the lamp M dims as more and more resistance is introduced into the lamp circuit.

Eventually, front contact iTS opens and back contact lTQ closes. At this point relays PI and P2 are energized inthe same manner as in the first transfer move. After P2 is energized, PI is deenergized, and after a predetermined time its contacts drop out. However, before this occurs, relay B is energized. The energizing circuit extends through contact ZTR, conductor I M front contact lTlEi, back contact GT9, conductor II I, front contact 3T2, contact lPi, conductor H9, contact lRM, conductor. tilt, contact 3BR, conductor l23, contact lES, conductor W5, and conductor i2 1. Relay B3 is now energized through contact 213, back contact ZEN, back contact 4136, back contact lBG and front contact 532. Lamp D3 is now extinguished.

Sufficient time has now elapsed so that front contact 21 i of relay Pl opens and back contact ZPl closes. Relay RCi is, therefore, energized through back contact iiPi, contact 2P2, conductor i29, contact E'iRll I, conductor till, back contact iRY and back contact ERR. Relay P2 is deep.- aized by the opening of iront contact 2H, and after a predetermined time, its contacts drop out. Moreover, relay BN is energized through contact @133 in the usual manner. Relays B2 and E2 become deenerglzed as has been explained several times above.

Now sufiicient time has elapsed so that the contacts of relay P2. open. Relay PI is new again energized in the circuit which has been traced through contact 'ZTR. It is to be noted that reenergized in circuits analogous to those traced with reference to the lamps of row a.

Sufficient time has now elapsed so that relay PI is deenergized. Relay ES is deenergized because front contact lBS opens. Relay EF ,is deenergized because back contact BF opens. When front contact 2PI opens, relay P2 is deenergized, and after a predetermined time, its contacts drop out. Relay B opens because contact IPI opens and relay RC2 closes through back contact 2PI, contact 2P2, conductor I 29, contact SRM, conductor I 3|, back contact IRY, front contact IRX and contact 2RCI The deenergization of relay B is followed by the deenergization of relay BN.

Relays BZ and E2 close in sequence in a manner explained with reference to the relays of row a. On the deenergization of relay RM, relay RMS is deenergized and after a predetermined delay, its contacts are opened. Relay TR, which was sealed in through contacts 3TB, JRM, conductor I 43, contact IER, conductor I33 and contact IRE, is deenergized because the holding circuit for relay TR is broken when contact 3RC2 opens and relay RM opens. Relay RY is energizedthrough front contact .IRMS, which has not as yet opened, conductor I39, contact IRC2, and relay RC2. Relay TIO, which was locked in through contact ZTR, now is deenergized. Relay BR, which was locked in through contact I TR, also opens.

Relay RX was energized through contact 2RY and it is deenergized when this contact opens. Relay RCI, also locked through contact 2RY, also opens. When relay TII) is deenergized, lamp M is deenergized and lamp P is energized.

Now su-flicient time has'elapsed and relay RMS drops out. The holding circuit for relay RC2 was closed through front contact IRMS and, therefore, this relay becomes deenergized. RY is also deenergized for the same reason. Relay Y, on the other hand, is energized through conductor H5, contact 22, conductor I45, contact lR2, and relay R2. Because contact 21 now opens, relay RI, sealed in through contact IRI, conductor in, relay X, contact ii? and conductor H5, opens. For the same reason, relay X is also deenergized. The second move by the machine is now complete. The relays which re main energized are AZ, BZ, BF, DS, DN, EZ, R2 and Y.

Player makes third play On the third play the player operates key PD only once. Relays D, D4 and DL are energized in the manner explained with reference to the other rows of lamps. Similarly lamp all is deenergized, relay DS is deenergized, relay DF is energized, and relays ES and EF are energized. On the release of button PD, relays D and DN are deenergized in sequence and relay DZ is energized and is followed by the deenergization of relay EZ. The relays which now remain energized are AZ, BZ, BF, DZ, DF, DL, EF, ES, R2, and Y. The array of rows is now as follows:

Row a 1= 2 Row D 3=2 +2 Row 0 0 Row d 3=2 +2 The zero power of 2 is now contained in the number of energized lamps in an odd number of rows and, therefore, the player has made an incorrect move.

Apparatus makes third movea correct more On the operation of button MTR, the apparatus makes a correct move since the player has moved incorrectly. The operation of button MTR' and conductor I49. Relay ARZ is now also ener- The energizing circuit for relay AR is the same .M circuit, lamp M. dims.

as for relay ARZ, except that it extends through contact I ARZ from conductor I53. When contact ICMS opens, the holding circuit for relay DL, through contact ZDL, conductor 81, contact I CMS, back contact IRMS, is opened and relay DL is deenergized. When relay TIO is energized, the lamp P is deenergized and lamp M is energized. Relays TI to T9 now become deenergized in sequence, and with a certain time delay and because of the addition of resistance in the lamp When relay T9 drops out, relay PI is energized through contact 2TR, conductor IOI, front contact ITIO, back contact ITS, conductor II I, and back contact 3P2. Relay P2 is next energized and because back contact 3P2 now opens, relay PI is deenergized and drops out after a certain time interval. However, in the meantime'relay A is energized in a circuit through contact 2TR, conductor IOI, front contact ITIO, back contact ITS, conductor III, front contact 3P2, contact IPI, conductor II9, contact ICM, conductor I55, contact ZAR, conductor III, and conductor I51. Relay A'I now is energized, deenergizing lamp a'l.

Now suflicient time has elapsed so that relay PI drops out. P2 is then deenergized but does not as yet drop out. However, the circuit through relay A is opened at contact IPI and relay A is deenergized. Relay AN is energized, relay AZ is deenergized, and relay EZ is energized in the manner which has been explained.

At this time relay P2 drops out and the holding circuit for relay CM, through contact 3CM, contact 3PI, conductor I33, and contact IRE, is opened, so that relay CM is deenergized. Relay TR which was locked in through contact 3TR and contact ICM is deenergized by the opening of contact 40M. Relay CMS is deenergized by the opening of contact 20M and it begins to drop out. While relay CMS is dropping out, relay TIO, which was sealed in through contact ZTR, becomes deenergized. Relay AR, which was sealed in through contact ITR, conductor I05, back contact IDR, back contact ICR, back contact IBR, and front contact IAR, is deenergized because its sealing circuit is open at ITR. Relay ARZ, which was sealed in the same circuit as relay AR through contact IARZ, is also deenergized. The dropping out of contact TIO results in the deenergization of lamp M and the energization of lamp P. Relay CMS drops out after lamp P is energized.

The relays which now remain energized are AN, BZ, BF, DZ, DF, EZ, EF and ES. Since there now remain three energized lamps in row b and three energized lamps in row a, the apparatus has clearly made a'correct move.

Player makes fourth move--an incorrect move The player can no longer make a correct move. He now elects to operate pushbutton PB twice. The first operation results in the deenergization of lamp b5, the energization of relay BN and the deenergization of relays BZ and EZ. The second operation results in the deenergization of lamp b6, the deenergization of relays BF, EF and EN, and the energization of relays BZ and EZ. The relays which are now energized are BL, BZ, DZ, DF, EZ and ES. There are now three lamps in row d and one lamp in row 17'.

Apparatus makes fourth move-a correct move The operation of the transfer button MTR now results in the energization of relays TR, TI to TI 0, CM and CMS in the manner explained. Relay DR is energized in the circuit extending through contact ITR, conductor I05, back contact IDR, back contact ICR, back contact IBR, back'contact IAR, conductor I01, front contact IES, back contact IEF, conductor I59, back contact 2AF, back contact 2BF, back contact ZCF, front contact. 2DF, and conductor ISI Relay BL is deenergized because contact ICMS is opened.

When front contact ITIO closes, relay TI is deenergized and relays TI to T9 drop out in sequence, each with a predetermined time delay. When relay T9 drops out, relays PI and P2 are closed in sequence and relay PI is thereafter deenergized but does not drop out. Relay D is now energized through contact ZTR, conductor I 0| front contact I TIO, back contact IT9, conductor III, front contact 3P2, contact IPI, conductor II 9, contact ICM, conductor I55, contact 2DR and conductor I63. Relay D5 is now energized and lamp d5 is deenergize'd. Thereafter contact I PI opens, relay D is deenergized, relay DN is energized and relays DZ and EZ are deenergized in sequence. Now relay P2 drops out.

However, relay CM remains energized through contact ZTR, conductor I0, front contact 2E8, back contact ZEF, conductor I05, contact ZRMS,

and conductor I49. Therefore, the stick circuit through contact 3TB for relay TR remains closed. Because contact 2TR thus remains closed, relays PI and P2 are again energized in sequence, and then deenergized in sequence with a certain time delay and lamp d6 is extinguished. Relay DF is now deenergized, relay EF is energized, and relays DZ and EZ are energized. Relay CM is now deenergized because its circuit through contact ZEF is opened. As a result, relay CMS is deenergized and begins to drop out. Relay TR is also deenergized as are relays TIO and DR. The lamp M is now extinguished and lamp P is energized. After lamp P is energized, relay CMS drops out. Only relays BZ, DZ, 'EZ, EF and ES remain energized and there is only one energized lamp in row b, and one energized lamp in row (1.

Player makes fifth move-an incorrect move Apparatus makes fifth move to win came The player now operates transfer button MTR and relays TR, TI to TIO, CM and CMS are energized while relay BL is deenergized. Relay tact IBZ and conductor I69.

and conductor DRZ is now energized through contact I'I'R, conductor I05, back contact IDR, back contact ICR, back contact IPR, back contact IAR, conductor IIl'I, front contact IES, front contact IEF, back contact IEZ, conductor I5I, back contact IAZ, back contact IBZ, back contact ICZ, con- Contact IDRZ is now closed and relay DR is energized through this contact in a circuit which is otherwise the same as the energizing circuit for relay DRZ.

After relay TIll is energized, relays TI to T9 are deenergized with the usual time delay and lamp M is energized and dimmed. When relay T9 drops out relays PI and P2 are energized in sequence and relay PI is deenergized and drops out after a predetermined interval of time. Because contact IPI and front contact 3P2 are closed, relay D is energized, relay D1 is energized and the last energized lamp d! is extinguished. The apparatus has now won the game.

Indicating and resetting operation Because all of the lamps al, b1, 01 and d? are deenergized, relay MW is energized in a circuit through contact 2A'l, contact ZB'I, contact 20?, contact 2Dl, conductor ill, and front contact IP2. The total games counter TP is energized through closed contact ZMW and, therefore, indicates that another game 'has been completed. The counter MWC, which indicates the number of games won by the apparatus is also energized through contact SMW. The lamps are also prepared for another game by the closure of relay S2i in a circuit through contact 4MW, conductor H3, back contact 3Q, back contact 3?, front contact 8N, conductor H5, contact 23, ill. Relay RE is energized through contact IIMW.

Relay S22 is energized because contact 352i is closed. Contact IRE is opened when relay RE is energized and, therefore, relay AI is deenergized because its holding circuit through contact iRE, conductor I33, conductor I15, contact till, is opened. ln-the same manner, relays BI, Cl and Di are deenergized and the corresponding lamps are energized. Because contact SAI is now open, relay AN, which was energized through conductor 55, contact 5A2, contact bill, and contact 3A, is deenergized. In the same manner, relays EN and CN are deen ergized. Relay CM, which was locked in through contact 3CM, is deenergized when contact tPi opens. Relay D is deenergized because its circuit is opened at contact iPl. Relay DH is deenergized because its holding circuit is opened at contact HTR, relay TR. being deenergized because its holding circuit is open at IRE. The holding circuit for relay DRZ is also opened at contact iTR. When PI is deenergized, P2 is also deenergized, but does not drop out.

The holding circuit for relay A2 is broken when front contact tAi is opened. The same is true of relays At and Ad. In the same manner, relays B2, B3, B l, C2, C3, C4, D2, D3 and D4 are deenergized and the corresponding lamps are energized. When relay TIE is deenergized, lamp M is deenergized and lamp P is energized. When relay CM is deenergized, relay CMS is deenergized since its holding circuit is opened. When front contact 2A2 opens, the sealing circuits for relays A5, A6 and A1 are opened and these relays are deenergized. In the same manner, re-

elapsed so that relay P2 drops out. Since relays Al, B1, C1 and D1 are deenergized, the circuit for relay MW is opened and it becomes deenergized. Relay RE is, therefore, deenergized and after a predetermined time interval it drops out. Moreover, counters TP and MWC are deenergized. Moreover, when relay S2I- was en ergized, relay P was energized in a circuit through contact 2Q, conductor I", contact I SZI, and relay S22. At this time relay CMS drops out. When relay P is energized, relay N is deenergized because its circuit is opened at contact 2?. For the same reason, relay SII is deenergized. Relay SIZ is opened up because contact 38 is opened. The contacts of S22 close and relays Al, A2, A3, A4, BI, B2, B3, DI and D2 are energized in the same manner as the corresponding relays were energized when relay SI2 was energized for combination No. 1. The corresponding lamps al, a2, a3, a4, bI, b2, 123, all and d2 are deenergized and the relays AZ, AF, BS,

CZ, CF, CS, DZ, BS, RN and EF are energized in preparation for a second game.

The apparatus is now prepared for another game. The array of energized lamps is, however,

diiferent than at the beginning of the first game.

In this case there are three lamps energized in row a, four in row 2), seven in row 0 and five in row d, corresponding to combination No. 2.

Another game may be repeated in the manner 1. In combination, a predetermined number of elements, each of said elements having a plurality of possible electrical conditions and means responsive to the condition of said elements and actuable only if the number of said elements in one of said conditions includes the nth power of r, where 'r is an integer and n is zero or an integer.

2. In combination, a predetermined number of elements, each of said elements having at least two possible electrical conditions and means responsive to the condition of said elements and actuable only if the number of said elements in one of said conditions includes the nth power of 2 where n is zero or an integer.

3. In combination, a predetermined number of elements, each of said elements having at least two possible electrical conditions, a separate circuit controlling means for each of the powers of 2 included in said number and means for actuating said circuit controlling means in dependance upon the powers of 2 included in the number of said elements that are in one of said conditions.

4. In combination, a predetermined number of elements, each of said elements having at least two possible electrical conditions, selective means for controlling the condition of said elements, a-

separate circuit controlling means for each of the powers of 2 included in said number and means responsive to said selective means for actuating said circuit controlling means in dependence upon the powers of 2 included in the number of said elements that are in. one of said conditions.

5. In combination, a plurality 01' sets of elements, each set having a predetermined number of like elements and each element having at least two possible electrical conditions, means responsive to the condition of said elements in said sets and actuable if the number of the elements in any set in one of said conditions includes the nth power of 2 where n is zero or an integer and means to be actuated by said responsive means when the sum of total number of occurrences of each power of 2 in all said sets is even.

6. In combination, a plurality of sets of elements, each set having a predetermined number of like elements and each element having at least two possible electrical conditions, means responsive to the condition of said elements in said sets and actuable in each of the powers of 2 included in the number of elements in one of said conditions occurs an even number of times in said sets.

7. In combination, a predetermined number of sets of elements, each of said elements having at least two possible electrical conditions and each set having a predetermined number of said elements, selective means for controlling the condition of said elements and means responsive to said selective means if each of the powers of 2 included in the number of elements in one of said conditions occurs an even number of times in said sets.

8. In combination, a predetermined number of sets of elements, each of said elements having at least two possible electrical conditions and each set having a predetermined number of said elements, selective means for controlling the condition of said elements, a circuit controller corresponding to each of the powers of 2 included in the number of elements in each said set, means responsive to said selective means for actuatin said circuit controller in dependence upon the powers of 2 included in the numbers of elements in said sets that are in a predetermined condition and means actuable by said responsive means if each of the powers of 2 included in the number of elements in said one of said conditions occurs an even number of times in said sets.

9. In combination, a plurality of sets of elements. each element having at least two electrical conditions and each set having a predetermined number of elements, selective means for initially maintaining certain of said elements in one of said conditions and certain others in another of said conditions, means for reverting all said elements to said other condition in a sequence which is predeterminable at will and means cooperative with said selective means after said elements have been reverted to said other conditions for reverting certain of said elements to said one of said conditions while the remainder are in said other condition, the number of said elements reverted to said one of said conditions being different than the number initially maintained in said one of said conditions.

10. In combination, a plurality of sets of elements, each said set having a predetermined number of elements and said elements having at least two conditions, means for altering the condition of the elements in each said set at will and means for preventing the alteration of the condition of the elements in any other set at will after the condition of the elements in one said set has been altered at will.

11. In combination, a plurality of sets of elements, each said set having a predetermined.

number of elements and said elements having at least two conditions, means for altering the condition of the elements in each said set at will, said altering means being operable repeatedly and including means cooperative with said elements for altering the condition of a different element in a set for each successive operation of said altering means, and means for preventing the alteration of the condition of one element in any other set at will after the condition of the elements in one said set has been altered at will.

12.-In combination, a plurality of sets of elements, each said set having a predetermined number of elements and said elements having at least two conditions, means for altering the condition of the elements in each said set at will, and means, responsive to the number of elements in a predetermined condition remaining in said sets after an alteration, for automatically altering the condition of said elements in said sets.

13. In combination, a plurality of sets of elements, each said set having a predetermined number ofelements and said elements having at least two conditions, means for altering the condition of the elements in each said set at will, and means, responsive to the number of elements in a predetermined condition remaining in said sets after an alteration, for automatically altering the condition of said elements in said sets,

said responsive means producing an alteration of one type when each of the powers of 2 included in the number of elements in one condition in said sets occurs an even number of times in said sets and an alteration of another type when any power of 2 included in the number of elements in said one condition occurs an odd number of times in said sets.

14. In combination, a plurality of sets of elements, each said set having a predetermined number of elements and said elements having at least two conditions, means for altering the conditionof the elements in each said set at will, means for preventing the alteration of the condition of the elements in any other set at will after the condition of the elements in one said set has been altered at will and means for automatically altering the conditions of the elements in said sets in response to the number of elements in one condition remaining in said sets after an alteration at will.

15. In combination, a plurality of sets of elements, each said set having a predetermined number of elements and said elements having at least two conditions, means for altering the condition of the elements in each said set at will, means for preventing the alteration of the condition of the elements in any other set at will after the condition of the elements in one said set has been altered at will and means for automatically altering the conditions of the elements in said sets in response to the number of elements in one condition remaining in said sets after an alteration at will, said automatically altering means producing an alteration of one type when each of the powers of 2 included in the number of elements in one condition in said sets occurs an even number of times in said sets and an alteration of another type when any power of 2 included in the number of elements in said one condition in said sets occurs an odd number of times in said sets.

16. In combination, a plurality of sets of elements, each said set having a predetermined number of elements and said elements having at

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