JPH09285642A - Puzzle - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a puzzle capable of restoring the original shape in several ways and having a player to recognize the logical regularity between small pieces, by joining puzzle pieces selecting from a synthetic puzzle piece, a different shaped puzzle piece, a divided different shape puzzle piece, and synthetic different shaped puzzle piece with areas as integer times large as a basic puzzle piece as a unit. SOLUTION: Four isosceles right triangles are to be a basic puzzle piece (a). A synthetic puzzle piece (b) is formed by a isosceles right triangle with an area as two times large as the basic puzzles piece (a), a synthetic puzzle piece (c) by a square with an area as two times large, a synthetic puzzle piece (d) by a rectangle with an area as four times, a synthetic puzzle piece (e) by a square with an area as four times, and a synthetic puzzle piece (f) by a triangle with an area as four times respectively. Unequal leg trapezoids produced by dividing a virtual symmetric different shaped puzzle piece made by removing a shape equal to the synthetic puzzle piece from a square as 8 times large as the basic puzzle piece into two pieces by the diagonal line are formed as divided different shaped puzzle pieces (g) and (g').

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention belongs to a puzzle.
The puzzle of the present invention can be freely created from a relatively gentle level to a level that requires extremely high thinking ability, and can be used as a teaching material for elementary geometry.

[0002]

2. Description of the Related Art Conventionally, a picture drawn on cardboard or the like is punched into a number of small pieces to be in a disjointed state, and a puzzle for arranging verification edges to restore the original picture, or a cardboard of a certain shape such as a square, etc. A puzzle that is cut into small pieces and restored to its original shape is known as a toy (Saikaihei 5-9589).
issue).

[0003]

However, in the conventional puzzle, it can be said that there are only a few methods for restoring a picture or shape, and even if the small pieces increase the complexity by being cut into small pieces, the original Interestingness decreases as the arrangement order for restoring the original picture or shape is stored, so that it becomes tired immediately.

In addition, when there are only a few restoration methods, the psychological effects of the player, especially the child, are mainly directed only to memorizing the various restoration methods. It can be said that it only contributes to the training of memory, and has little effect in developing logical thinking and a sense of mental balance. Also, because there is no logical law between the shapes of each small piece, even when targeting children,
It does not have the effect of developing thinking ability by comparing each piece.

Therefore, it is an object of the present invention to be able to restore the original shape in any number of ways, thereby making it possible to think of multiple solutions and to recognize the logical law between the pieces. To provide a puzzle.

[0006]

In order to achieve the above object, the puzzle of the present invention has a base length x, an equal side length y, and an apex angle 2π.
/ N (n is an integer), a group of basic puzzle pieces consisting of isosceles triangles, a group of composite puzzle pieces composed by circumscribing a plurality of basic puzzle pieces so that their sides completely overlap each other, one composite A variant puzzle piece created by stacking on a puzzle piece another synthetic puzzle piece or a basic puzzle piece that has the same interior angle and can be included in the composite puzzle piece so that one interior corner is completely coincident with each other and the overlapping portion is removed. , A group of divided variant puzzle pieces generated by dividing the variant puzzle piece along its diagonal or centerline, and a plurality of variant puzzle pieces or divided variant puzzle pieces circumscribed so that their sides completely overlap each other. It is a puzzle piece selected from the group of synthetic variant puzzle pieces that are synthesized by combining the puzzle pieces with line symmetry into any number of non-axisymmetric puzzle pieces. If there is an even number, and for the divided variant puzzle pieces and the synthetic variant puzzle pieces, the regularity of the number of the variant puzzle pieces that can be combined without excess or deficiency by circumscribing the other divided variant puzzle pieces or the composite variant puzzle pieces Arrange each colored puzzle piece, X or Y on one side
(X and Y are integer multiples of x and y, respectively) forming a regular n-gon.

In the puzzle of the present invention, a basic puzzle piece is used as a unit, and a synthetic puzzle piece having an integral multiple area thereof, a variant puzzle piece derived from the synthetic puzzle piece, a divided variant puzzle piece, and a synthetic variant puzzle piece are selected and combined. Various restoration methods are possible. Therefore, it is possible to visually learn area calculation and similar shapes.

When only one of the basic puzzle piece, the synthetic puzzle piece and the irregular puzzle piece is selected, the synthetic puzzle piece and the irregular puzzle piece are obtained without cutting the basic puzzle piece. The regular n-gon can be easily constructed by various restoration methods. In addition, even when selecting a divided variant puzzle piece or a composite variant puzzle piece, the number is limited to the number of composite variant pieces that can be combined without excess or deficiency by circumscribing other divided variant puzzle pieces or composite variant puzzle pieces. Therefore, the regular n-sided polygon can be configured.

The number of puzzle pieces to be selected may be arbitrary if it is axisymmetric, but it is limited to an even number if it is axisymmetric, so at least one restoration method is a line-symmetric figure. Can be. Therefore, it is possible to expect a shape having a logical law such as a line-symmetrical figure, a point-symmetrical figure, or a figure in which a certain shape is periodically continuous in a certain direction as the shape to be restored.

Further, each puzzle piece is regularly colored. For example, if puzzle pieces with the same area have the same color, it contributes to the training of thinking power of area calculation, and if puzzle pieces with the same shape have the same color, it is useful for studying similar shapes. Further, if even numbered puzzle pieces of the same shape and the same color are arranged, the puzzle pieces of the same color are symmetrically arranged, which is useful for training a sense of mental balance and an aesthetic sense.

[0011]

BEST MODE FOR CARRYING OUT THE INVENTION The material constituting the puzzle piece is paper,
Any material such as plastic, ceramics, and metal that can hold a predetermined shape may be used. In this case, a regular n-sided frame material having the same size as the contour of the completed puzzle should be provided. Further, the puzzle of the present invention is not limited to the one made of substances that can be combined on a desk, but may be software that is stored in a storage medium as a computer program and combined on a monitor.

The above n is preferably 4 or 6. When n = 4, the basic puzzle piece is an isosceles right triangle, so
As synthetic puzzle pieces derived from it, symmetrical geometric figures with a high degree of freedom of combination such as isosceles right triangles, squares, rectangles and isosceles trapezoids can be created. n = 6
In this case, since the basic puzzle piece becomes an equilateral triangle, it is possible to create a symmetric figure having a high degree of freedom of combination such as an equilateral triangle, a rhombus, and an isosceles trapezoid as a synthetic puzzle piece derived from it. The higher the degree of freedom of combination, the greater the number of restoration methods.

[0013]

EXAMPLES Example 1 This is an example of a puzzle of the present invention in which n = 4 and X = 4x, and is composed of a basic puzzle piece, a composite puzzle piece, and a divided variant puzzle piece. This embodiment will be described with reference to the drawings. FIG.
[FIG. 6] is a diagram showing one arrangement state of the puzzle of the first example.

In the puzzle of this example, four right-angled isosceles triangles a having an isosceles length x and a base length y are basic puzzle pieces. Then, b, c, d, e, and f are synthetic puzzle pieces. The composite puzzle piece b is an isosceles right triangle having a double area of the basic puzzle piece a, and the number thereof is four. The composite puzzle piece c consists of a square having the same double area, and the number is 2. The composite puzzle piece d is composed of a rectangle having an area four times larger than that of the other puzzle piece, and the number is one. The composite puzzle piece e is composed of squares each having an area four times as large as that of the composite puzzle piece e. The synthetic puzzle piece f is composed of right-angled isosceles triangles having the same area four times, and the number thereof is one. Therefore, the total number of synthetic puzzle pieces is nine.

Next, g and g'are divided variant puzzle pieces, respectively, from a virtual composite puzzle piece consisting of a square of 8 times the area of the basic puzzle piece a to a composite puzzle piece consisting of a square of the same area of 4 times. It consists of an unequal trapezoid formed by dividing a line-symmetrical virtual variant puzzle piece generated by excluding e by the diagonal line in the center. The divided variant puzzle pieces g and g ′ have the same shape as the other by inverting one. That is, the two are line-symmetrical to each other.

In the puzzle of this example, the arrangement state can be changed as shown in FIG. As is apparent from FIG. 2, the divided variant puzzles g and g ′ are the same as the virtual composite puzzle piece composed of right-angled isosceles triangles having an area eight times as large as that of the basic puzzle piece a.
It is also possible to regard a line-symmetrical virtual variant puzzle piece generated by removing the composite puzzle piece f composed of right-angled isosceles triangles having a double area by dividing the puzzle piece into two equal parts at the center line.

According to the puzzle of this example, a synthetic puzzle piece c
By using the same color as that of the synthetic puzzle piece d and that of the synthetic puzzle piece d, it is possible to complete a line-symmetrical figure in a predetermined frame as shown in FIG. Of course, there are many other combinations. In addition, since the vertex angle of the basic puzzle piece a is a right angle and the synthetic puzzle pieces have the same area, or the area is an integral multiple of the basic puzzle piece, the figures having different shapes have the same area. The reason can be explained visually by overlapping the basic puzzle piece a on the figure. For this reason, children can easily understand the area calculation.

-Example 2- This is an example of a puzzle of the present invention in which n = 4 and X = 4x, and is composed of a basic puzzle piece and a divided variant puzzle piece. This embodiment will be described with reference to the drawings. FIG. 3 is a diagram showing one arrangement state of the puzzle of the second embodiment.

The puzzle of this example has 16 right-angled isosceles triangles a and a'having an isosceles length x and a base length y as basic puzzle pieces. However, 8 of the 16 basic puzzle pieces a and the remaining 8 basic puzzle pieces a ′ are color-coded. Hereinafter, unless otherwise specified, the basic puzzle piece a will also refer to the basic puzzle piece a ′. And h and i
Each is a puzzle piece divided into different shapes, and even if both are inverted, the same shape and color are formed.

Divided odd-shaped puzzle pieces h and i are virtual composite puzzle pieces corresponding to f of Embodiment 1 (an isosceles right triangle having a quadruple area of the basic puzzle piece a) and b of Embodiment 1 (i.e., 2).
A virtual irregular puzzle piece having an irregular trapezoidal shape (corresponding to g in Example 1) generated by removing a virtual composite puzzle piece corresponding to a double-area right-angled isosceles triangle) is divided into two by its diagonal line. It is a triangle that is non-axisymmetric with each other.
Among them, the eight triangles located on the upper base side of the unequal-leg trapezoid are the divided variant puzzle pieces h, and the eight triangles located on the lower bottom side are the divided variant puzzle pieces i.

As is apparent from FIG. 3, since the puzzle of this example looks like a windmill, it contributes to the training of the aesthetic sense of the player and also allows the player to enjoy the creativity. Furthermore, the puzzle of this example can change the arrangement state as shown in FIG. In the arrangement state of FIG. 4, the child can learn a similar shape in addition to the area calculation.

EXAMPLE 3 This is an example of the puzzle of the present invention in which n = 4 and Y = 4y, and is composed of a basic puzzle piece, a divided variant puzzle piece, and a synthetic variant puzzle piece. This embodiment will be described with reference to the drawings. FIG. 5: is a figure which shows one arrangement state of the puzzle of 3rd Example.

In the puzzle of this example, 32 right-angled isosceles triangles having an equilateral length x and a base length y are used as basic puzzle pieces. However, each of the 16 basic puzzle pieces a and a ′ is color-coded with each other. Hereinafter, unless otherwise specified, the basic puzzle piece a refers to all the basic puzzle pieces a and a ′. Then, j and k are a divided variant puzzle piece and a composite variant puzzle piece, respectively.

The divided variant puzzle piece j is an inequality caused by removing the basic puzzle piece a from the virtual composite puzzle piece corresponding to b (the isosceles right triangle having a double area of the basic puzzle piece) of the first embodiment. It is a triangle on the upper base side of two non-axisymmetric triangles formed by dividing a trapezoidal virtual variant puzzle piece (similarly reduced form of g of Example 1) by two diagonal lines, The number is 32.

The synthetic variant puzzle piece k has two lower triangles (one of which is inverted) of the above two triangles.
Is a line-symmetrical quadrangle that is generated by circumscribing with the non-vertical leg side of the original unequal leg trapezoid, and the number is 16.

In the puzzle of this example, diamond-shaped gems seem to be scattered in the arrangement state of FIG. However, the arrangement state of this puzzle can be changed as shown in FIGS. 6 and 7. In FIG. 6, four windmills appear to rotate side by side, and in FIG. 7, the fifth windmill appears to be protruding toward the center of the four windmills. Although illustration is omitted, the puzzle of this example can describe up to nine windmills in this way. Therefore, it contributes to the training of a sense of balance and an aesthetic sense.

-Example 4- This is an example of a puzzle of the present invention, in which n = 4 and X = 6x, and is composed of a basic puzzle piece and a composite puzzle piece. This embodiment will be described with reference to the drawings. FIG. 8 is a diagram showing one arrangement state of the puzzle of the fourth embodiment.

Also in the puzzle of this example, four right-angled isosceles triangles a having an isosceles length x and a base length y are basic puzzle pieces. Further, b, c, e, and l to r are synthetic puzzle pieces, respectively, and the total number thereof is 22.

The composite puzzle piece b (same shape as the composite puzzle piece b of Example 1) is a right-angled isosceles triangle having a double area of the basic puzzle piece, and the number thereof is four. Synthetic puzzle piece c
(The same shape as the composite puzzle piece c of Example 1) and the composite puzzle piece 1 each consist of a square and a parallelogram having the same double area, and the number of each is 2. Synthetic puzzle pieces m and n
Consists of an isosceles trapezoid and an isosceles trapezoid of the same triple area, and the number of each is 2. Synthetic puzzle pieces e (the same shape as the synthetic puzzle piece e of Example 1), o and p are composed of squares, parallelograms and isosceles trapezoids each having the same quadruple area, the number of which is 2 each.
It is. The synthetic puzzle piece q is a line-symmetrical figure formed by circumscribing two parallelograms that are twice as large as each other on their short sides, and the number is two. Synthetic puzzle piece r is 2
It consists of a line-symmetrical figure that is generated by circumscribing two double parallelograms at their long sides, and the number is two. It is obvious that the puzzle of this example can also have various array states other than the point-symmetrical array state as shown in FIG. 8, but the illustration is omitted.

Embodiment 5 This is a book composed of a basic puzzle piece, a composite puzzle piece, a variant puzzle piece, a divided variant puzzle piece, and a composite variant puzzle piece, with n = 6, X = Y = 4x = 4y. It is an example of an invention puzzle. This embodiment will be described with reference to the drawings. FIG. 9 shows the fifth
It is a figure which shows one arrangement state of the puzzle of an Example.

Unlike the previous four embodiments, the puzzle of this example uses six regular triangles A having a side length x (= y) as basic puzzle pieces. B and C are composite puzzle pieces, D is a variant puzzle piece, E and f are divided variant puzzle pieces, and G is a composite variant puzzle piece.

The composite puzzle piece B is an equilateral triangle having an area four times as large as that of the basic puzzle piece A, and the number thereof is six. The composite puzzle piece C is a parallelogram having a double area of the basic puzzle piece A, and the number is 6. Therefore, the total number of composite puzzle pieces is 12. The odd-shaped puzzle piece D is an isosceles trapezoid formed by removing the basic puzzle piece A from the regular triangular composite puzzle piece B having an area four times as large as that of the basic puzzle piece, and the number is 6.

The divided irregular-shaped puzzle pieces E and F are formed of the triangles on the lower bottom side of the two types of triangles formed by dividing the above-mentioned irregular-shaped trapezoidal irregular-shaped puzzle piece D by one of the diagonals, and the number thereof is 6 for each. Split variant puzzle pieces E and F
Is the same as the other if one is inverted. That is, the two are line-symmetrical to each other.

The synthetic variant puzzle piece G is based on the triangle of the upper base side and the triangle line-symmetrical with the triangle of the two types formed by dividing one of the above isosceles trapezoidal variant puzzle pieces D by one diagonal line. Is a line-symmetrical figure generated by circumscribing the legs of an isosceles trapezoid.

The puzzle of this example can have various symmetrical arrangement states as shown in FIGS. 10 to 14 in addition to the symmetrical arrangement states as shown in FIG. Therefore, the puzzle of this example contributes to the training of a sense of balance by creating various line-symmetrical figures and point-symmetrical figures within a predetermined framework. For example,
It is advisable to have the children restore the line-up or point-symmetrical arrangement when restoring. In addition, it is possible to give the player the joy of discovering the principle of order hidden in chaos.

[0036]

As described above, in the puzzle of the present invention, the original shape can be restored by a number of methods, so that the puzzle can be enjoyed for a long time. In addition, it is possible to develop a logical thinking ability and a sense of mental balance by making a plurality of solution methods to be considered and recognizing a logical law between small pieces. Further, the puzzle of the present invention can be used not only as a toy but also as a teaching material for elementary geometry.

[Brief description of drawings]

FIG. 1 is a diagram showing one of arrangement states of a puzzle according to a first embodiment.

FIG. 2 is a diagram showing another arrangement state of the puzzle of the first embodiment.

FIG. 3 is a diagram showing one of arrangement states of a puzzle according to a second embodiment.

FIG. 4 is a diagram showing another arrangement state of the puzzle of the second embodiment.

FIG. 5 is a diagram showing one of arrangement states of the puzzle according to the third embodiment.

FIG. 6 is a diagram showing another arrangement state of the puzzle of the third embodiment.

FIG. 7 is a diagram showing another arrangement state of the puzzle of the third embodiment.

FIG. 8 is a diagram showing one of arrangement states of the puzzle according to the fourth embodiment.

FIG. 9 is a diagram showing one of arrangement states of the puzzle of Example 5;

FIG. 10 is a diagram showing another arrangement state of the puzzle of the fifth embodiment.

FIG. 11 is a diagram showing another arrangement state of the puzzle according to the fifth embodiment.

FIG. 12 is a view showing another arrangement state of the puzzle of the fifth example.

FIG. 13 is a diagram showing another arrangement state of the puzzle according to the fifth embodiment.

FIG. 14 is a diagram showing another arrangement state of the puzzle according to the fifth embodiment.

[Explanation of symbols]

 a, A Basic puzzle piece b, c, d, e, f, B, C Composite puzzle piece D Variant puzzle piece g, g ', h, i, j, E, F Divided variant puzzle piece k, G Composite variant puzzle Piece

Claims (13)

[Claims] 1. A group of basic puzzle pieces consisting of isosceles triangles having an isosceles length x, a base length y, and an apex angle of 2π / n (n is an integer), and a plurality of basic puzzle pieces are arranged so that their sides completely overlap each other. A group of synthetic puzzle pieces that are combined by circumscribing to each other, one synthetic puzzle piece having the same interior angle and another synthetic puzzle piece or basic puzzle piece that can be included in the synthetic puzzle piece A group of odd-shaped puzzle pieces created by overlapping and removing overlapping portions so as to match, a group of divided odd-shaped puzzle pieces created by dividing the odd-shaped puzzle piece along its diagonal or centerline, and a plurality of odd-shaped puzzle pieces or A puzzle piece that is selected from the group of composite variant puzzle pieces that are composed by circumscribing divided variant puzzle pieces so that their sides completely overlap each other. For any number of non-axisymmetric puzzle pieces, even number for non-axisymmetric puzzle pieces, and for divided variant puzzle pieces and synthetic variant puzzle pieces by circumscribing with other divided variant puzzle pieces or synthetic variant puzzle pieces Is arranged so that each puzzle piece colored with regularity is arranged so as to form a regular n-sided polygon of one side X or Y (X and Y are integer multiples of x and y, respectively). A featured puzzle. 2. The puzzle according to claim 1, wherein n = 4. 3. The puzzle according to claim 2, wherein the puzzle pieces selected are a basic puzzle piece, a synthetic puzzle piece, and a divided variant puzzle piece. 4. The number of basic puzzle pieces is four, and the number of composite puzzle pieces is four right isosceles triangles having twice the area of the basic puzzle pieces, two squares having the same double area and four square areas. Rectangle 1
A total of 9 squares, each of which has a square area of 4 times the area and one isosceles triangle of the same size of 4 times the area. The number of divided variant puzzle pieces is 8 times the area of the basic puzzle piece or an isosceles right triangle. A line-symmetrical variant puzzle piece created by removing a square or right-angled isosceles triangle composite puzzle piece of 4 times the same area from the composite puzzle piece The puzzle according to claim 3, wherein there is one unequal leg trapezoid, and X = 4x. 5. The puzzle according to claim 2, wherein the puzzle pieces selected are a basic puzzle piece and a divided variant puzzle piece. 6. The number of basic puzzle pieces is 16, and the number of divided irregularly shaped puzzle pieces is a synthesis of a right-angled isosceles triangle having a double area from a composite puzzle piece having an area four times as large as that of the basic puzzle piece. The non-asymmetrical trapezoidal variant puzzle piece generated by removing the puzzle piece is divided into two by its diagonal line, and each is two triangles of two kinds which are non-axisymmetric to each other, and X = 4x. Described puzzle. 7. The puzzle according to claim 2, wherein the puzzle pieces selected are a basic puzzle piece, a divided variant puzzle piece, and a synthetic variant puzzle piece. 8. The number of basic puzzle pieces is 32, and the number of divided variant puzzle pieces is an unequal leg generated by removing the basic puzzle piece from a composite puzzle piece of an isosceles right triangle having a double area of the basic puzzle piece. A trapezoidal variant puzzle piece is divided into two diagonal lines, and the two triangles that are non-axisymmetric to each other have 32 triangles on the upper base side. The number of composite variant puzzle pieces is the lower triangle of the above two triangles. The puzzle according to claim 7, wherein 16 triangles which are line-symmetrical and are formed by circumscribing two side triangles with the non-vertical leg sides of the original unequal leg trapezoid, and Y = 4y. 9. The puzzle according to claim 2, wherein the puzzle pieces selected are a basic puzzle piece and a synthetic puzzle piece. 10. The number of basic puzzle pieces is four, and the number of composite puzzle pieces is four right-angled isosceles triangles having a double area of the basic puzzle pieces, and two square and parallelogram each having a double area. And 3 times the same area of each isosceles trapezoid and unequal leg trapezoid
Same as the square, parallelogram and isosceles trapezoid each having the same quadruple area, and two parallelograms having two parallelograms that are twice as large as each other and circumscribed at their short sides. 10. The puzzle according to claim 9, wherein a total of 22 pieces including two line-symmetrical figures that are generated by circumscribing two parallelograms that are twice as long as each other on their long sides, and X = 6x. 11. The puzzle according to claim 1, wherein n = 6. 12. The puzzle according to claim 11, wherein the selected puzzle pieces are a basic puzzle piece, a composite puzzle piece, a variant puzzle piece, a divided variant puzzle piece, and a composite variant puzzle piece. 13. The number of basic puzzle pieces is 6, and the number of composite puzzle pieces is 6 equilateral triangles having an area four times as large as that of the basic puzzle pieces and 6 parallelograms having twice the area of the basic puzzle pieces. 12 pieces in total, the number of odd-shaped puzzle pieces is 6 which is an isosceles trapezoid generated by removing the basic puzzle piece from a composite puzzle piece of an equilateral triangle having an area four times as large as that of the basic puzzle piece, and the number of divided odd-shaped puzzle pieces is the same as above. Of the two types of triangles that are formed by dividing a trapezoidal variant puzzle piece by one of its diagonals, the lower-bottom triangle and six triangles that are line-symmetrical to it are the same. A line-symmetrical figure 6 that is generated by circumscribing the upper base triangle and the line-symmetrical triangle of the two types of triangles formed by dividing the odd-shaped puzzle piece by one diagonal line with the original isosceles trapezoid leg. The number is X, and X = Y = 4x = 4y. Puzzle described in 2.