CN88206228U

CN88206228U - Maths intelligence chess

Info

Publication number: CN88206228U
Application number: CN 88206228
Authority: CN
Inventors: 王巨兴
Original assignee: Individual
Current assignee: Individual
Priority date: 1988-05-25
Filing date: 1988-05-25
Publication date: 1988-12-21

Abstract

The mathematic intelligence chess is composed of n+[2](n>or=3) chess pieces and a chessboard; the number on the chess pieces is one number of n+[2](n>or=3); with no repetition; n+[2](n>or=3) is a positive integer arithmetic progression with the tolerance >or=1; the chessboard has a square chess position zone with N+[2](N>or=n) square chess positions. The utility model can develop people's mathematic intelligence, foster people's can and quick thinking, and adapt to various ages and people who have different educational attainments and intelligence levels. The utility model can be produced in large quantity, having the advantages of simple manufacture and low cost.

Description

Maths intelligence chess

The utility model is a kind of mathematics intelligence educational chess, by arrange differentiations of the chess piece that has numeral through certain rule, makes the arrangement of numeral reach a kind of rule state, thus develop in education with in enjoying and the raising people in the intelligence and wisdom aspect the mathematics.

Mathematics intelligence educational chess of the present utility model is made up of chess piece and chessboard.This chess piece add up to n ²Individual, n is the positive integer more than or equal to 3, and each chess piece is marked with a numeral, and n ²Number constitutes a tolerance more than or equal to 1 arithmetic progression.

n ²N on the individual chess piece ²Number can be to begin counting since arbitrary positive integer of 1, with since 1 counting for well.

The shape of chess piece can be got different shape, as cube, rectangular parallelepiped, cylindrical, the hexagonal cylindricality, anistree cylindricality or the like, with square for well.But also can make the artwork ornaments as human or animal's form of different shape.

Numeral on the chess piece can only be illustrated on the surface as upper surface, also can be illustrated on several or all surfaces, as for the square chess piece, numeral is marked on 6 same surfaces.

All chess pieces can adopt a kind of color, can make with method of the general material of making chess piece such as plastics, porcelain, mosaic, celluloid, glass, timber, mao bamboon, marble or the like, but as odd number chess piece (refer to subscript numeral for odd number) and even numbers chess piece (refer to subscript numeral be even numbers) with two kinds of different colors, preferably contrast the words of tangible two kinds of colors, as white and black, rouge et noir or the like, then can in playing chess, arrange by chess piece, discharge the pattern of various beauties, both increased the interest of playing chess, the pattern of discharge also can be done the reference of fine arts design.

On chessboard, if the foursquare center of forming with the chess position is a symcenter, put on four axis of symmetry with strikingly color, chess bit region is divided into eight districts of 45, then more help arriving the target that this game chess chess piece is arranged smoothly by the mobile chess piece of certain rule.

The arranging of this chess chess piece will finally reach and make each horizontal stroke of being positioned on the chessboard, craspedodrome and equal all as the subscript numeral addition summation of the chess piece on cornerwise two straight lines (being n chess piece) that same scope (being the first number and the tail figure place of n number arithmetic progression) with n and n is relevant fixes a number really, and this numerical value is called common value.Think that this dish chess " is mediated " this moment.

Above on the said n chess piece digital sum be easy to calculate with following formula.

n ²Number summation=(the first number of ordered series of numbers+tail figure place)/2 * n ²

Common value=(n ²The number summation)/(n)

As work as n=5, n ²For from 25 integers of 1～25 time, can be regarded as 25 number total value=325, each row, row, the common value of five numbers=65 on the diagonal line.

When educating or enjoying, choosing has N accordingly ²The chessboard of individual chess position is illustrated in figure 1 as the chessboard of N=9, is marked with I, II, III, four axis of symmetry of IV, divides several zones at 45 chessboard at chessboard, wherein I and II quadrature, III and IV quadrature.Chess piece is arranged and is mainly comprised following steps:

1. cloth chess

Indicating n ²The n of individual integer ²Individual chess piece is arranged on the chess position by digital size order, and so-called order can be from left to right or from right to left, selects voluntarily from top to bottom or from top to bottom again.

Therefore one to have eight kinds of cloth chess methods available:

From top to bottom, from left to right;

From top to bottom, from right to left;

From left to right, from top to bottom;

From right to left, from top to bottom;

From top to bottom, from left to right;

From top to bottom, from right to left;

From left to right, from the bottom to top;

From the bottom to top from right to left.

2. decide rotation center

When n was odd number, the chess piece that can be on the center of the board chess position was a rotation center, and the numeral on this chess piece should be a number relevant with the tail figure place with the first number of ordered series of numbers, can be calculated by following formula:

Numeral on the chess position, center on the chess piece=(the first number of ordered series of numbers+tail figure place)/2

When n is even number, then with the central point of chessboard be rotation center or suppose a mark number is arranged in this in the heart is 0 chess piece, be rotation center with this chess piece of supposing.

3. the displacement draw in chess of chess piece mediates

Mediating of chess will realize that the displacement of chess piece can be adopted distinct methods, but in order to reach the purpose of mediating chess rapidly, introduce several effective chess piece displacement modes here according to each one creativity by the displacement of chess piece.

A. circumference rotation displacement

This step moves on on the new chess position for a certain through a pair of on the symmetric position of center or several chess piece is rotated to an angle in 360 ° of scopes of circumference simultaneously mutually on the axis of rotation center being in.

B. parallel cross transposition

To be in up and down or about two rows go up symmetry two couples totally four chess pieces carry out parallel cross transposition mutually to arrive on the new chess position, as shown in Figure 2,2a represents to have and optional refers to that as chess 7(chess piece subscript number is 7 chess piece, below roughly the same), chess 25,

chess

12,30 4 chess pieces of chess are on the two rows of symmetry, with chess 7 parallel shifted to chess 25 positions, chess 25 cross transposition are to chess 12 positions, chess 12 parallel shifted are to chess 30 positions, and chess 30 cross transposition form cloth chess shown in Fig. 2 b at last to chess 7 positions.More than four steps orders can exchange arbitrarily, because of being

chess

7 and 12 translations,

chess

25,35 intersections are moved, so be expressed as a

chess

7,12,25,35 one groups are carried out parallel cross transposition.

C. square crossing displacement

To be in up and down or left-right symmetric two row on two couples totally four chess pieces, as shown in Fig. 3 a, be optional chess 2, chess 5, chess 32, chess 35 carry out square crossing displacement mutually, chess 2 cross transposition to chess 35 positions, chess 35 vertically moves on on chess 32 positions, chess 32 intersections move on on chess 5 positions, and chess 5 vertically moves on on chess 2 positions, forms new cloth chess situation shown in Fig. 3 b.Because of being that vertical movement has been carried out in chess 5 draw in chess 35,

chess

2 and 32 has carried out cross transposition, carries out the square crossing displacement so be expressed as a

chess

5,35,2,32.

D. parallel shifted and vertical movement

To be in up and down or symmetrical two row on, two pairs totally four chess pieces carry out parallel or vertical movement, shown in Fig. 3 c.Wherein,

chess

4 and 76,6 and 78 two pairs carry out parallel shifted; And

chess

28 and 36,46 and 36,54 two pairs carry out vertical movement.

Among above b～d, the order of each step is unrestricted, carries out but must be one group with four chess pieces of above-mentioned requirements.

E. the mutual transposition of chess piece

Chess and another have another chess piece on certain corresponding relation (as vicinity, rotational symmetry, center symmetric relation) to intercourse the position.

This chess residence complex mathematical is converted among education enjoys, and is not only toy, also can make the experimental teaching aid of science and education, because along with the change of n number is big, the difficulty that chess piece is arranged also deepens thereupon, so can adapt to the enjoying of people of various ages and cultural intellectual level, accomplish that each takes what he needs, appeal to both the more and the less cultured, help people and improve intelligence, temper one's willpower, cultivate quick thinking, and this chess is easy to make, and is with low cost, is suitable for producing by batch.

To be described in further detail the method for mediating of the utility model mathematics intelligence educational chess and the draw in chess of chess piece arrangement method thereof by embodiment below.

To be described in further detail the arrange method of mediating of draw in chess of the utility model mathematics intelligence educational chess and chess piece by embodiment below.

The synoptic diagram of a chessboard when Fig. 1 is n=9 and a cube chess piece;

Fig. 2 a is parallel cross transposition method synoptic diagram with 2b;

Fig. 3 a and 3b are square crossing displacement method synoptic diagram;

Fig. 3 c is parallel shifted and vertical movement method synoptic diagram;

Fig. 4 a, 4b, 4c is the arranging and mediate synoptic diagram of chess during n=3 among the embodiment 1;

Fig. 5 a, 5b, 5c is the arranging and mediate synoptic diagram of chess during n=5 among the embodiment 2;

Fig. 7 a, 7b, 7c is the arranging and mediate synoptic diagram of chess during n=9 among the embodiment 3;

Fig. 8 a, 8b is the arranging and mediate synoptic diagram of chess during n=4 among the embodiment 4;

Fig. 9 a-c is the arranging and mediate synoptic diagram of chess during n=6 among the embodiment 5;

Figure 11 a-c is the arranging and mediate synoptic diagram of chess during n-10 among the embodiment 6;

Figure 11 d is the cloth chess synoptic diagram of embodiment 7;

Figure 12 is the cloth chess synoptic diagram of embodiment 8.

Embodiment 1: this chess has n ²=9 chess pieces and one have N ²=n ²The chessboard of the chess bit region of=9 square chess positions.Numeral on 9 chess pieces is 1～9 positive integer.

n ²The cloth chess of=9 chess pieces is shown in Fig. 4 a.Deciding rotation center is chess 5.Begin the circumference rotation displacement of chess piece then;

ⅰ. rotate (clockwise direction change 225 ° or counterclockwise to changeing 135 °) being in the axis of symmetry I that is mutually quadrature and the chess piece on the II (being respectively 1 and 9 and 3 and 7) respectively around symcenter chess 5, cloth chess situation (the former chess that is arranged in these lattice is represented with the same as shown in the last figure in the space among the figure, below roughly the same) shown in 4b on this moment chessboard;

ⅱ. original chess piece (being respectively 2 and 8 and 4 and 6) on axis of symmetry III that is mutually quadrature and IV is rotated forward 45 ° (or reverse 315 °) around chess 5 respectively, and this moment, cloth chess situation was shown in Fig. 4 c.For extremely, this coils n is that 3 chess is mediated to this.Promptly all chess piece numeral summations that are on the straight line equate, are equal to a relevant number in ordered series of numbers interval with n and n number, this common value=15 herein, promptly

Embodiment 2: this chess has n ²=25 chess pieces and one have N ²=n ²The chessboard of the chess bit region of=25 square chess positions.Numeral is 1～25 positive integer on 25 chess pieces.

Cloth chess situation such as Fig. 5 a.Deciding rotation center is chess 13.

The chess piece that at first will be in during with the chess piece rotation displacement on axis of symmetry I and the II rotates forward 225 ° (or reverse 135 °) respectively around chess 13, this moment, cloth chess situation was shown in Fig. 5 b, to be in then on axis of symmetry III and the IV chess piece around chess 13 rotate respectively forward 135 ° (or reverse 225 °) then chess mediated, cloth chess situation is shown in Fig. 5 c at this moment, and the common value that each straight line (totally 12) is gone up the chess piece addition is 65.

Embodiment 3, and this chess has n ²=81 chess pieces and one have N ²=n ²Numeral on the chessboard of the chess bit region of=81 square chess positions, 81 chess pieces is 1～81 positive integer.Cloth chess such as Fig. 7 a.Fixed 41 is the rotation center chess.

Rotation displacement:

Chess piece on axis of symmetry I, the II is rotated forward 225 ° (or reverse 135 °) respectively around chess 41, the chess piece on axis of symmetry III, the IV is rotated forward 135 ° (or reverse 225 °) respectively around chess 41, the cloth chess situation of this moment is shown in Fig. 7 b.

Getting 4,76 and 6,78 of symmetry is one group and carries out parallel shifted.

Getting 28,36 and 46,54 of symmetry is one group and carries out vertical movement.

Getting 13,15,67,69 and 22,24,58,60 of symmetry respectively is one group and carries out parallel cross transposition by mode shown in Fig. 2 a respectively.

Getting 29,47,35,53 and 30,48,34,52 of symmetry and respectively be one group carries out square crossing by mode shown in Fig. 3 a respectively and is shifted.

The situation of cloth chess is shown in Fig. 7 c at this moment.The chess of n=9 is mediated, on promptly whole 20 straight lines on the chess piece digital addition equal common value 369.

Certainly this step of cross transposition also can realize by rotation displacement, grasps but angle control is difficult.

Embodiment 4: this example has n ²=16 chess pieces and one have N ²=n ²The chessboard of the chess bit region of=16 square chess positions.Numeral on 16 chess pieces is 1～16 positive integer.The cloth chess of chess piece is shown in Fig. 8 a.With 0 of hypothesis on Fig. 8 a is

rotation center.Chess

2 and 15,3 and 14,5 and 12, the 8 and 9 four pairs of chess pieces with the chess 0 of hypothesis be must be newly behind each Rotate 180 of center ° cloth chess situation shown in Fig. 8 b.At this moment, this chess is mediated, and is promptly vertical, horizontal diagonal line on totally 10 straight lines on the chess piece digital addition equal common value 34.

Embodiment 5: this example has n ²=36 chess pieces and a N ²=n ²The chessboard of the square chess bit region of=36 square chess positions.Numeral is the positive integer from 1～36 on 36 chess pieces.The cloth chess of 36 chess pieces is shown in Fig. 9 a.With chess

33、34、3、4，

7、12、25、30，

20,23,14,17 respectively be taken as one group, carry out parallel cross transposition respectively, displacement back chess piece is arranged as Fig. 9 b.

Again with chess

18、24、13、19，

5、35、2、32，

10,28,9,27 respectively be taken as one group, carry out the square crossing displacement respectively, displacement back chess piece is arranged as Fig. 9 c.

Fig. 9 d merges Fig. 9 b and Fig. 9 c situation of arranging and forms.Arrive this, the chess of n=6 is mediated, and the situation of arranging of all chess pieces is shown in Fig. 9 e.Promptly on the chess piece on totally ten four longitudinal and transverse, diagonal line digital sum equal common value 111.

Embodiment 6: this example has n ²=100 chess pieces and N is arranged ²=n ²The chessboard of the square chess bit region of=100 square chess positions.Numeral on 100 chess pieces is the positive integer from 1～100.

Chess piece is arranged shown in Figure 11 a, and rotation center is 0 point of hypothesis.

With 40 chess pieces of following 20 pairs of symmetries respectively with 0 be the center forward or 180 ° of retrograde rotations:

3，98；4，97；7，94；8，93；13，88；14，87；17，84；18，83；21，80；31，70；61，40；71，30；22，79；32，69；62，39；72，29；24，77；27，74；33，68；38，63。

Following tetrad totally two groups of chess pieces carry out the square crossing displacement respectively:

6,96,5,95 and 16,86,15,85.

Following tetrad totally two groups of chess pieces carry out parallel cross transposition respectively:

51,60,41,50 and 52,59,42,49.

After having implemented following several steps, cloth chess situation such as Figure 11 b.

Again following six pairs of chess pieces are exchanged displacement mutually:

25,26; 48,58; 80,30; 70,40; 8,3 and 7,4.

This moment, cloth chess situation was shown in Figure 11 c.Chess is mediated.Totally 22 in longitudinal and transverse, diagonal angle straight line, on each straight line on the chess piece digital sum be equal to common value 505.

This chess is being enjoied the chess piece that Shi Keren gets n the consecutive numbers that a first number begins, or n chess piece that becomes the number of arithmetic series, shown in following examples.

Embodiment 7:

Shown in A part among Figure 11 d,, get 16～60 n according to the cloth chess of Figure 11 a among the embodiment 6 ²=25 chesses with reference to the method for mediating of embodiment 2, can be mediated this chess, common value=190.

Shown in B part among Figure 11 d,, get 62～95 n according to the cloth chess of Figure 11 a among the embodiment 6 ²=16 chesses with reference to the method for mediating of embodiment 4, can be mediated this chess, common value=314.

Examples of implementation 8:

Referring to cloth chess shown in Figure 12, the n that gets ²Numeral constitutes the arithmetic series of from 11 to 59 tolerance=2 on=25 chess pieces, can mediate this chess with reference to the method for mediating of embodiment 2, common value=175.

Claims

1, a kind of digital intelligence education is played chess, it is characterized in that by the n that indicates a positive integer respectively ²(n 〉=3) individual chess piece and one are contained N ²(chessboard of the square chess bit region of the individual square chess of N 〉=n) position is formed said n ²Positive integer on the individual chess piece constitutes the arithmetic progression of tolerance 〉=1.

2, as the said mathematics intelligence educational chess of claim 1, it is characterized in that said n ²Numeral on the individual chess piece is from 1～n ²Continuous positive integer.

3, as claim 1 or 2 said mathematics intelligence educational chess, it is characterized in that said n ²Numeral on the individual chess piece is n from 3～10 n ²The number of individual formation arithmetic progression.

4,, it is characterized in that chess piece can be that square, xsect are foursquare rectangular parallelepiped or right cylinder as claim 1 said mathematics intelligence educational chess.

5,, it is characterized in that odd number chess and even numbers chess are with different surface colors as claim 1 said mathematics intelligence educational chess.

6, as claim 1 said mathematics intelligence educational chess, it is characterized in that being marked with the center symmetric points at chessboard is four axis of symmetry of symcenter, chess bit region is divided into eight districts of 45.