JP2001276413A - Puzzle and block group - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a puzzle and a block group allowing a player to play and learn mathematics under logical consideration. SOLUTION: This puzzle comprises a plurality of blocks of a polyhedral shape and a box having a cubic internal space in which three perpendicular planes and three planes opposite to them are separately divided, respectively. The same cube as the internal space of the box can be formed by assembling the blocks. Each block group has rectangular solid blocks including a block equal in length on three perpendicular sides, three blocks equal in length on two sides, and six blocks different in length on three sides.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD The present invention belongs to puzzles and blocks.

[0002]

2. Description of the Related Art Conventionally, a puzzle having a plurality of blocks and being able to assemble and play these blocks in a given three-dimensional shape from different states has been known as a toy.

[0003]

However, in the conventional puzzle, if the completed product is moved or held after assembling the blocks, the assembled blocks collapse. Therefore, it is not possible to view the entire solid formed after the assembly, and thus it is not possible to consider the mathematical relationship between the solid and each block, the geometrical properties of each block, and the like. Therefore, an object of the present invention is to provide a puzzle and a group of blocks that can be played and can learn math by thinking logically.

[0004]

A puzzle according to the present invention comprises a plurality of polyhedral blocks, a box having an internal space forming a cube, and three mutually orthogonal surfaces of the internal space and three opposing surfaces thereof. And a box divided so as to be separate from each other, and the same cube as the internal space of the box can be constituted by assembling the blocks.

[0005] The puzzle of the present invention comprises a plurality of polyhedral blocks and a box whose internal space forms a cube. When the blocks are assembled, the same cube as the internal space of the box can be formed. Can be stored inside. The box is divided so that the three surfaces orthogonal to each other in the internal space and the three surfaces facing these are separate from each other. Thus, by opening one of the separate boxes of the box, one can look at the three faces of the cube made up of blocks, and by turning around and opening the other of the box, one looks at the three opposing faces. be able to.
That is, in the puzzle of the present invention, the entire finished product can be viewed after assembling the blocks. Therefore, it is possible to think while looking at the completed product, and as a result, it is possible to understand mathematical rules such that, for example, the volume of a polyhedron such as a triangular pyramid is proportional to the base area and its height.

As an example of the puzzle of the present invention, the blocks are:
The blocks are all rectangular parallelepiped and are orthogonal to each other.
N types of cubic blocks each having a side length Ls (s = 1, 2,... N, n is a natural number of 2 or more);
The lengths of three sides orthogonal to each other are Ls, Ls, and L, respectively.
t (t = 1,2, ··· n , where s is different from the.) in which _n P ₂ types of each three square prism block, Ls each lengths of three sides which are perpendicular to each other, Lt and Lu (U = 1,
2,... N, but different from s and t. ) _N C ₃ consists kinds of rectangular blocks each 6 to be, the internal space of the box, the length of the side there is a puzzle that constitutes a cube of L1 + L2 + ··· + Ln.

In this puzzle, the work of assembling blocks to form a cube can be represented by one identity. This will be described as an example when n = 3. When n = 3, all the blocks form a rectangular parallelepiped whose side length is one of L1, L2 and L3. The types and numbers of the blocks are as follows.
Here, L1 = a, L2 = b, and L3 = c are replaced.

[0008] As for the cubic block, a block having three sides orthogonal to each other with lengths of a, a and a (hereinafter, referred to as blocks {a, a, a}), blocks {b, b, and b}, respectively. b} and block {c,
There are three types, c and c, respectively. For a square prism block, block {a, a, b}, block {a, a,
c}, block {b, b, a}, block {b, b,
c}, block {c, c, a}, and block {c,
c, 6 types ₍₃ P ₂ kinds) of b} is the three. For the rectangular parallelepiped block, one of the blocks {a, b, c} (
₃ C ₃ types) is six each.

Since the volume of a rectangular parallelepiped is the product of the lengths of three sides orthogonal to each other, the volumes of the above blocks are, in order, a ³ , b ³ , c ^{3 for} a cubic block, and a ² b, a ^{2 for} a square block. c, ab ² , b ² c, ac ² , bc ² , and abc for a rectangular parallelepiped block. On the other hand, when a block is assembled, a cube having sides of a + b + c can be formed, and the volume of the cube is (a + b +
c) ³ . Therefore, forming a cube from blocks can be represented by the following identity.

(Equation 1)

According to the puzzle of n = 3, the player can understand the upper identity while playing. In addition, since the above identity is an expression indicating factorization, the player can understand the general property of factorization. When n = 3, the general properties of identities and factorization can be similarly understood.

In this puzzle, the length of the side is L1 + L2 +
.. Can be enjoyed by assembling the blocks so as to form not only a cube of + Ln but also a cube or a rectangular parallelepiped smaller than this. Further, the length L1 of the side of the block,
L2,... Ln are represented by L2 = 2L1 and L3 = 3.
When L1,... And Ln = nL1, it is possible to increase the variations of solids that can be configured, and it is possible to configure solids of the same shape in several ways. Therefore,
Players will not get tired of playing this puzzle for a long time. In this puzzle, it is preferable to change the color of the block for each type of block. When the color of the block is changed in this way, the design can be enjoyed after the block is assembled, and the user can easily think about the geometrical properties of the block.

The block group of the present invention is a block having a rectangular parallelepiped shape, and the lengths of three sides orthogonal to each other are all L.
s (s = 1, 2,... n, n is a natural number of 2 or more), each one of n types of cubic blocks and 3 orthogonal to each other
The lengths of the sides are Ls, Ls and Lt (t = 1, 2,
.. N, but different from s. ), And the lengths of three orthogonal sides of _n P ₂ types of square blocks and three sides orthogonal to each other are respectively different from Ls, Lt and Lu (u = 1, 2,... N, where s and t are different). ), Each of which is composed of six _n C ₃ types of rectangular parallelepiped blocks. According to this block group, the above-described effects can be obtained.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION The puzzle of this embodiment is composed of 27 blocks and boxes. FIG. 1 is a perspective view showing a puzzle block of the embodiment.

In this embodiment, all the blocks have a rectangular parallelepiped shape, and the length of each side is any of a, b, and c. Here, b = 2a and c = 3a. The block is divided into three by a combination of the lengths of three sides orthogonal to each other.
It is classified into a cubic block having all the same side lengths, a square block having two sides having the same length, and a rectangular parallelepiped block having all three sides having different lengths. The specific combinations and numbers are as follows.

As for the cubic block, there are three types of blocks {a, a, a}, blocks {b, b, b}, and blocks {c, c, c}. For the square block, a block {a, a, b}, a block {a, a, c}, a block {b, b, a}, a block {b, b, c}, a block {c, c, a} , and six ₍₃ P ₂ kinds) of the block {c, c, b} is the three.
As for the rectangular parallelepiped block, there are six types ( ₃ C ₃ types) of one of the blocks {a, b, c}. In this embodiment, the colors of the blocks are different for each type.

By assembling these 27 blocks, a cube having sides of a + b + c can be formed as shown in FIG. Since the volume of a cube or other rectangular parallelepiped is the product of the lengths of three sides orthogonal to each other, FIG.
It can be expressed by the following identity that a block having the side lengths of a + b + c is formed by the blocks shown in FIG. Therefore, according to the present embodiment, the player can understand the lower identity while playing.

(Equation 2)

According to the present embodiment, one block {a, a, a}, one block {b, b, b}, three blocks {a, a, b}, and three blocks {a, a, b} Block ｛b,
From b, a｝, a cube having side length a + b can be formed. Since this can be expressed by the identity below, the player can also learn about this identity.

(Equation 3)

Further, in this embodiment, a cube having a side length of b + c and a cube having a side length of a + c can be formed by assembling appropriate blocks.
Therefore, it is possible to learn the identities of (b + c) ³ and (a + c) ³ . Further, by arranging the blocks in a plane, the lengths of the sides are a + b + c, a + b,
b + c and a + c squares can each be constructed, so that (a + b + c) ² , (a + b) ² , (b +
c) ^2, and (a + c) can learn about identities about ^2. In addition, in the present embodiment, a rectangular parallelepiped and a rectangle can be configured.

As described above, in this embodiment, various shapes can be formed by assembling the blocks. Moreover, the length of the side of the block is b = 2a and c =
3a, there are quite a lot of configurable shapes,
In addition, there are several ways to assemble the blocks for construction. Therefore, the player does not get tired of playing the puzzle of the present embodiment for a long time, and can understand the relationship between assembling blocks to form a cube and performing factorization while playing. Furthermore, the fact that the number of blocks is 27 in total can be explained by the relationship of {the number of block side lengths (a, b, c)} ³ = 3 ³ = 27. You can also learn about relationships.

Next, the puzzle box of the present embodiment will be described. FIG. 2 is a perspective view showing a puzzle box. The box 1 is divided into a first case 1A and a second case 1B having the same shape. In each of these cases 1A and 1B, three plates are joined so as to be orthogonal to each other, and the shape of the inner surface of each of the three surfaces is a square having side lengths of a + b + c. Therefore, when the box 1 is closed together with the two cases 1A and 1B, the internal space of the box 1 becomes a cube having sides of length a + b + c. Therefore, in this embodiment, it is possible to assemble the 27 blocks shown in FIG.

Then, of the six faces of the cubic body assembled and constructed, three faces orthogonal to each other are placed in the second case 1B.
3 can be seen as shown in FIG.
By opening A, it can be seen as in FIG. That is, according to the box 1, the entire cube can be viewed after assembling the blocks. Therefore, it is possible to think about the above-mentioned identities and the like while looking at the whole. In the present embodiment, as shown in FIGS. 3 and 4, blocks of the same type can be symmetrically arranged, and the colors of the blocks are different for each type. You can enjoy sex.

[0022]

According to the puzzle and block group of the present invention, it is possible to play and to learn mathematics by thinking logically.

[Brief description of the drawings]

FIG. 1 is a perspective view showing blocks of a puzzle.

FIG. 2 is a perspective view showing a puzzle box.

FIG. 3 is a perspective view showing an assembled state of puzzle blocks.

FIG. 4 is a perspective view showing an assembled state of puzzle blocks.

[Explanation of symbols]

 1 box 1A first case 1B second case

Claims (5)

[Claims] 1. A box having a plurality of polyhedral blocks and a box having an internal space forming a cube, wherein three surfaces orthogonal to each other in the internal space and three surfaces facing these are separated from each other. A puzzle, comprising: a closed box; and, by assembling blocks, the same cube as the internal space of the box can be formed. 2. The blocks are all rectangular parallelepiped blocks, and the lengths of three sides orthogonal to each other are all Ls (s = 1, 2,...).
.. N, where n is a natural number of 2 or more), each of n types of cubic blocks, and lengths of three sides orthogonal to each other are Ls, Ls, and L, respectively.
n (t = 1, 2,... n, but different from s) _n P Each of three types of square block of _two types and three sides orthogonal to each other have lengths of Ls, Lt, and L, respectively.
u (u = 1, 2,... n, but different from s and t)
_N C ₃ types of rectangular parallelepiped blocks, each having 6 blocks, and the inner space of the box has a side length of L1 + L2 +... + Ln
The puzzle according to claim 1, wherein the puzzle is a cube. 3. L2 = 2L1, L3 = 3L1,.
3. The puzzle according to claim 2, wherein Ln = nL1. 4. The puzzle according to claim 2, wherein the colors of the blocks are different for each type. 5. Blocks each having a rectangular parallelepiped shape, wherein the lengths of three mutually orthogonal sides are all Ls (s = 1, 2,...).
.. N, where n is a natural number of 2 or more), each of n types of cubic blocks, and lengths of three sides orthogonal to each other are Ls, Ls, and L, respectively.
n (t = 1, 2,... n, but different from s) _n P Each of three types of square block of _two types and three sides orthogonal to each other have lengths of Ls, Lt, and L, respectively.
u (u = 1, 2,... n, but different from s and t)
A block group comprising 6 each of _n C ₃ types of rectangular parallelepiped blocks.