JP7295356B2 - educational dice - Google Patents

Description

The present invention enhances computational ability through a simple dice game, and at the same time, the intellectual discovery that repeated predetermined calculations and dice operations always converge to the same color can be obtained, thereby stimulating interest in arithmetic and mathematics. It provides an educational dice that can be held and how to use it.

Already proposed is a learning method in which numbers are written on a polyhedral die and calculations are performed using the resulting numbers. (For example, Patent Document 1)
It has also been proposed to put numbers and arithmetic symbols on dice and combine the resulting numbers and arithmetic symbols into a calculation puzzle. (For example, Patent Document 2)

JP 2006-230629 Actual Kaihei 6-57391

In the prior art, even if calculation problems and puzzles can be created randomly with dice, the calculation results themselves do not impress or lead to new intellectual discoveries, and there is no motivation or interest to enjoy and continue calculations on one's own. The problem was that it didn't last long.

In the present invention, in polyhedral dice with 10 or more sides on which 10 kinds of numbers from 0 to 9 are described, only a specific number group, the number itself or the surface on which it comes out is colored with a common color. characterized by

Using the dice of the present invention, a finite number of iterations of a given calculation and dice operation will always arrive at the result that all dice rolls are of the same color. This utilizes the properties of integers, and with the dice of the present invention, the properties of integers can be felt and understood through one's own calculations and dice manipulations.

This wonder and intellectual discovery will keep children and adults interested in repeating calculations and rolling dice. By doing so, it becomes possible to cultivate computational power and activate the brain, and it may even be the beginning of an interest in the study of mathematics.

The dice of claim 1 are for handling three-digit integers.
Specifically, when dealing with three-digit integers, only the three numbers 4, 5, and 9 are colored with a common color (temporarily called color A) for the numbers themselves or the surface on which the numbers appear. For other numbers, the number or the side on which it appears is colored with a color other than A.

For numbers other than 4, 5, and 9, it is preferable to use a color clearly different from the A color. Also, the numbers other than 4, 5, and 9 do not have to be the same color, and may be divided into appropriate groups and painted in B color, C color, and so on. Rather, by painting in multiple colors other than A, you can be aware of the random results when rolling the dice, and the way the results converge to color A after the calculation operation creates a more impressive effect. preferable.

For example, if the colors are clearly different from each other, such as red for A, blue for B, yellow for C, etc., the visual effect will be clearer and the effect provided by the present invention will be greater. preferable.

The same three colored dice are rolled in this way, and the calculations and dice operations described in detail after paragraph number 0017 are performed.

The dice of claim 2 are for handling four-digit integers.
Specifically, when dealing with 4-digit integers, only the four numbers 1, 4, 6, and 7 are colored with a common color (temporarily called color A) for the numbers themselves or the surface on which they appear. do. For other numbers, the number or the side on which it appears is colored with a color other than A.
Hereinafter, the selection of colors and effects are the same as the examples already described in paragraphs 0009 to 0010.

The same four colored dice are rolled in this way, and the calculations and dice operations described in detail after paragraph number 0017 are performed.

The dice of claim 3 is one kind of dice and can handle both 3-digit and 4-digit integers.
Specifically, only the five numbers 1, 4, 5, 6, 7, and 9 are colored with a common color (temporarily called color A) on the numbers themselves or on the surface on which the numbers appear. For other numbers, the number or the side on which it appears is colored with a color other than A.
Hereinafter, the selection of colors and effects are the same as the examples already described in paragraphs 0009 to 0010.

When dealing with a three-digit integer with the dice of claim 3, three dice are rolled and the following calculations and dice operations are performed. When dealing with a 4-digit integer, roll 4 dice and perform the calculations and dice operations described in detail from paragraph number 0017 onwards.

However, although this dice has the advantage that it can be used for both 3-digit integers and 4-digit integers, there are inevitably many numbers or faces colored in A, so the calculation operation reaches the result. There is a disadvantage that the wonder and visual effect at the time of doing so are diluted.

Next, a detailed description will be given of the calculation method and dice operation performed using the dice provided by the present invention.

First, a dice handling three-digit integers in claim 1 will be described as an example.
The numbers 4, 5, and 9 of the dice are colored in the same color (hereinafter referred to as color A), and the other numbers are colored in a color other than A.

First roll the same three dice and check the results.
For example, let's say you get three numbers: 8, 0, and 4. Since only 4 out of 3 dice are A color, only 1 A color has appeared at this stage. In addition, if the first three rolls are the same number, the roll is invalidated and rerolled. This is because the difference between the maximum integer and the minimum integer explained below becomes zero, and the calculation operation becomes meaningless.

Now perform the following calculations and dice operations. Keeping the results of the three dice, rearrange them in descending order to make the largest integer, and rearrange them in ascending order to make the smallest integer. If the result contains a 0, the most significant digit is 0 when making the smallest integer. In that case, it is treated as an integer starting with a number other than 0 below that digit.
In this example, the largest integer is 840 and the smallest integer is 048 (= 48).

Take the difference between the largest and smallest integer thus obtained. That is, the calculation is performed by subtracting the smallest integer from the largest integer. Mental arithmetic is preferable, but if it is difficult, you can do it by writing.
For this example, the answer is 840-48=792.

Depending on the answer, change the roll of the dice to get sides 7, 9, and 2. Since only 9 is A color, there is only one A color at this stage.

A series of calculations and dice operations described in paragraphs 0020 to 0022 are repeated until the answer converges.

We will continue to explain this example in detail. The dice in this state are subjected to the same calculation and dice operation as described in paragraph number 0020 . That is, the three dice are rearranged while maintaining the outcome to produce the largest and smallest integers.
For this example, the largest integer is 972 and the smallest integer is 279.

For the maximum and minimum integers obtained in this manner, the same calculations as described in paragraph 0021 are performed. That is, the calculation is performed by subtracting the smallest integer from the largest integer.
For this example, we get the answer 972-279=693.

As already mentioned in paragraph 0022, the number of the dice is changed according to the answer, and faces 6, 9, and 3 are obtained. Since only 9 is A color, there is only one A color at this stage.

Furthermore, the series of calculations and dice operations described in paragraphs 0020 to 0022 are repeated.

This example will be explained in detail next. The dice in this state are subjected to the same calculation and dice operation as described in paragraph number 0020 . Perform the same computational operation on the dice in this state. Since the largest integer is 963 and the smallest integer is 369, we get 963-369=594 as the result of subtraction.

Depending on the answer, change the roll of the dice to get a 5, 9, or 4 side. Then, since these three numbers are of A color, it can be confirmed that all three dice are of A color.

Furthermore, the series of calculations and dice operations described in paragraphs 0020 to 0022 are repeated.

Perform the same computational operation on the dice in this state. Since the largest integer is 954 and the smallest integer is 459, the result of subtraction is 954-459=495. Even if you check the result of the dice according to the answer, all three are A color as well.

After that, even if the same calculation operation is repeated, the answer remains unchanged at 495, and all three dice still show the A color.

Here, calculations and dice operations were explained using the example of the case where the numbers 8, 0, and 4 appeared when the dice were rolled for the first time. , converges to the same result. However, as already mentioned, if the first three rolls are the same number, they will be invalidated and rerolled.

Since this is based on the properties of integers, as long as the initial three numbers are not the same number, repeating the series of calculations and dice operations described in paragraphs 0020 to 0022 a limited number of times will converge to the same integer. When using the dice of the present invention, different colors appear at first, but when a series of calculations and dice operations are repeated, all sides are always aligned to color A, and the situation does not change after that. Experience discovery.

As for the dice handling 4-digit integers in claim 2, the number of dice to be rolled is 4, and the calculation is only the subtraction of 4-digit integers.
The numbers 1, 4, 6, and 7 of the dice are colored with the same color (hereinafter referred to as color A), and the other numbers are colored with a color other than A.

First, check the roll of the same 4 dice. In addition, if the first four rolls are the same number, they are invalidated and rerolled. This is because the difference between the maximum integer and the minimum integer explained below becomes zero, and the calculation operation becomes meaningless.

For example, suppose the initial rolls were 3, 0, 5, and 9. Here, it is a 4-digit integer, but in the same way as in the case of the 3-digit integer already described in paragraphs 0020 to 0022, the maximum and minimum integers are obtained, the difference between them is calculated, and a dice operation is performed.

In this example, we get 9530-359=9171.
Furthermore, the same calculation and dice operation are repeated. Then the obtained integers are sequentially
9711-1179=8532
8532-2358=6174
7641-1467=6174
and converge to 6174, and remain unchanged thereafter. Therefore, all four dice rolls are A.

Here, calculations and dice operations were explained using the case where the numbers 3, 0, 5, and 9 appeared as the numbers when the dice were rolled for the first time. Any combination of four numbers other than 9 will converge to the same result. However, as already described, if all four initial rolls are the same number, the roll will be invalidated and rerolled.

Since this is based on the properties of integers, as long as the initial four numbers are not the same number, repeating the series of calculations and dice operations described in paragraphs 0020 to 0022 a limited number of times will converge to the same integer. When using the dice of the present invention, different colors appear at first, but when a series of calculations and dice operations are repeated, all sides are always aligned to color A, and the situation does not change after that. Experience discovery.

The dice of claim 3 can handle both 3-digit and 4-digit integers.
When dealing with a three-digit integer, three dice are rolled and the series of calculations and dice operations described above are performed. When dealing with a 4-digit integer, roll 4 dice and perform the same series of calculations and dice operations. In either case, the result is that all the dice are rolled in A color.

If you want to start with easy calculations, just deal with 3-digit integers. If three dice according to claim 1 or three dice according to claim 3 are used, the above-mentioned series of calculations and dice operations are performed to reach the intellectual discovery that all the dice will always have the same color.

Six dice can also be used as a device to facilitate the calculation. Three dice are first rolled to create a three-digit integer, but in subsequent calculations, the maximum and minimum three-digit numbers can be placed in the upper and lower two rows as dice rolls.

As a further ingenuity, 9 dice are used, and if the maximum number, the minimum number of 3 digits, and the result of the subtraction are placed in the upper and lower 3 rows as the results of the dice, the calculation will be easy and the calculation will be possible.

Intellectual discovery that even when dealing with a 4-digit integer, the dice of claim 2 or 4 dice of claim 3 are used, and the above-described series of calculations and dice operations are performed to ensure that all the dice have the same color. to reach

Eight dice can also be used as a device to facilitate the calculation. Four dice are first rolled to create a four-digit integer, but in subsequent calculations, the maximum and minimum four-digit numbers can be placed in the upper and lower two rows as dice rolls.

As a further ingenuity, 12 dice are used, and the maximum number, the minimum number of 4 digits, and the result of subtraction are placed in the upper and lower 3 rows as dice results, making calculation easy and verification possible.

The dice of the present invention have the role of displaying each digit of a 3- to 4-digit integer. If a 10-sided dice is used, numbers from 0 to 9 are written on each side, but the shape of the dice need not be limited to 10-sided, and any polyhedron with 10-sided or more can be used to form the dice of the present invention. .

For example, in the case of using a dodecahedron, even if 10 numbers from 0 to 9 are written on each of the 10 sides, 2 sides remain. On the remaining two sides, write nothing, or write some symbol or pattern other than numbers, and roll the dice with those sides again until you get a number again. Alternatively, any of the numbers 0 through 9 may be printed again on the remaining two sides. The probabilities of rolling each number are no longer the same, but this does not significantly interfere with the objectives of the present invention.

Using the dice of the present invention, when a series of calculations and dice manipulations are repeatedly performed, all faces are always aligned with the color A. Utilizing this phenomenon, it is possible to devise ways to play tricks, predictions, fortune-telling, etc. can.

For example, let the target opponent roll the dice of the present invention and say, "I will show you that all sides of the dice are colored A", and instruct the opponent to perform the above-described series of calculations and dice operations. If you repeat it multiple times, it will all match A color, so it will look like a magic trick or a prophecy to your opponent.

For example, let the target opponent roll the dice according to the present invention, and say, "Fortune-telling is performed based on the color of the face of the dice. If you match color A, you will have good luck. If you match color B, you will be lucky. If you match color C, you will be unlucky." , instruct the other party to perform the above-mentioned series of calculations and dice operations. If you repeat it multiple times, all of them will match the A color, so it looks like a fortune-telling result to the other party.

By repeating the above-described series of calculations and dice operations using the dice described in claim 1, 2, or 3, it is possible to repeat the practice of subtracting three-digit or four-digit integers while having fun. It is possible to naturally cultivate computational power.

Also, if the subtraction calculation is correct every time, the numbers or sides of the dice will always be the same color after a finite number of times, and after that, no matter how many times the same calculation operation is repeated, the resulting integer will be the same integer. Experiencing this wonder arouses intellectual curiosity. And since the dice are re-rolled from the beginning many times to try to confirm the phenomenon, they can repeat the calculation of 3-digit or 4-digit subtraction with interest. They learn much more because they are willing to do the calculations rather than being forced to solve a number of simple calculation drills.

Furthermore, it is interesting to note that repeating this computation always converges to the same integer after a finite number of iterations. This is due to the properties of integers, but with the dice of the present invention, it is possible to enjoy a part of mathematics called number theory. It can provide an opportunity to become familiar with the profound academic field of mathematics.

Furthermore, by using the dice of the present invention, if the above-described series of calculations and dice manipulations are repeated, the dice numbers or sides will always be of the same color. You can also devise a way to play.

It is an example of the dice of the present invention. This is an example in which the dice for three-digit integers described in claim 1 is configured as a decahedron, and 10 numbers from 0 to 9 are written on each face. The 4th, 5th, and 9th faces are colored in a common color (assumed to be color A), and the other number faces are colored in colors other than A. 1 shows a view from above, and FIG. 2 shows a view from below.

It is an example of the dice of the present invention. This is an example in which the dice for three-digit integers described in claim 1 is configured as a decahedron, and 10 numbers from 0 to 9 are written on each face. The numbers 4, 5, and 9 are colored in a certain common color (assumed to be color A), and the other numbers are colored in colors other than A. 3 shows the case viewed from above, and FIG. 4 shows the case seen from below.

1 The top surface is colored A. 2 The body surface is colored A. 3 The body surface is not colored A. 4 The ridgeline between the body surfaces. 5 Ridges between the top surface and the body surface 6 Bottom surface, the surface is other than A color 7 Ridge line between the bottom surface and the body surface 8 Numbers are colored in A color on the top surface 9 Body surface 10 The number is colored in A color 10 The number is other than A color on the body side 11 The number is other than A color on the bottom side

Claims (3)

A polyhedral dice having 10 or more sides, each side having one of 10 numbers from 0 to 9 printed on it, and each number printed on at least one side. , 4, 5, 9 or faces 4, 5, 9 are colored in the same common color, and the other digits or faces are colored in a different color. A polyhedral dice having 10 or more sides, each side having one of 10 numbers from 0 to 9 printed on it, and each number printed on at least one side. , 1, 4, 6, 7 or the faces 1, 4, 6, 7 are colored in the same common color, and the other digits or their faces are colored in a different color. A polyhedral dice having 10 or more sides, each side having one of 10 numbers from 0 to 9 printed on it, and each number printed on at least one side. , 1, 4, 5, 6, 7, 9 or faces 1, 4, 5, 6, 7, 9 are colored in the same common color, and the other digits or faces are colored in a different color. Dice being played.

Images