Cube I. Cube shape and the number of rooms
Cube consists of a huge cube and a layer of shell outside the cube. There is a certain space between the two. The big cube also contains many small cube rooms. Similar to Rubik's Cube. Cube has only one exit. Only when you reach the room connecting the shell and the inner cube can you get out of the Cube. This room is called the "bridge" in the movie. The edges of each room are 14 feet (slightly longer than 4 meters). Each side of the big cube has the length of 26 rooms, so the total size is 26*26*26=17576 rooms. (But in fact there are not so many rooms, because the room must have a certain amount of space to move)
II. How to identify whether there are traps in the
room · Identify whether the room is safe
Each room in the Cube is marked with three three-digit numbers. Because the number of each room is different, Holloway initially thought it was the serial number of the room (she therefore thought there were hundreds of millions of rooms, but she was wrong). Leaven then thought that they could use these three three-digit numbers to identify if there were any traps in the room. Leaven’s memory was very good. She wrote down the number of each room they passed. After summarizing, she came to the conclusion: usually three There are traps in rooms with prime numbers in numbers (this theory worked well at the beginning, but later there were traps in rooms without prime numbers, so this theory was overturned). The truth was finally unearthed at the end of the film: it is not prime numbers that identify the trap, but powers of prime numbers. Leaven asked Kazan to report the prime factor of each number.
·The power of prime numbers
Every natural number (1, 2, 3, 4...) can be obtained by multiplying prime numbers if it is not a prime number, such as 120=2*2*2*3*5. If the order of prime numbers is not taken into account, this notation is unique. Now expressed in the form of power, 2*2*2 is expressed as 2^3 here, so 120= (2^3) *3*5. If a number contains only one prime factor, then it is a prime number power. Obviously every prime number itself is a prime number power (this also explains why Leaven's theory did not go wrong in the first place). But the power of a prime number is not necessarily a prime number, for example, 27=3*3*3=3^3, but 27 is not a prime number, because it can be expressed as 3 times 9. In this case, Leaven's theory failed.
III. Spatial position and moves the room
regardless of whether there is a trap room, three three-digit numbers do not represent themselves, after the following presentation you will find that they represent the spatial location and the trajectory of the room.
·The coordinates of the room
The number of each room is actually Cartesian coordinates, which represents the location of the room in space, but it is different from Cartesian coordinates, and the two coordinates can be converted to each other. For example: the Cartesian coordinates of a room are 493,454,967, then its X-axis coordinate is 4+9+3=16, Y-axis coordinate is 4+5+4=13, and Z-axis coordinate is 9. +6+7=22, so the rectangular coordinates of this room are (16, 13, 22), where the coordinate unit is a room, so in the Z-axis direction, this room is four rooms away from the shell. The coordinate value cannot be a negative number (because the addition of three natural numbers cannot become a negative number), the coordinate value in each direction of XYZ will not be greater than 26 (except for the "bridge"). Leaven and the others once reached a room with a Y-axis coordinate of 27, which is actually a "bridge" to the outside of the Cube. But they didn't discover the secret at the time, because the room was still surrounded by other rooms, and it was not until after Worth was thrown by Quentin into the room where Rennes had died before and saw that there was nothing outside of the passage, and he figured out the original room. Will move. He said: "It is not we are moving, but the room.... This can explain why we have been feeling the shock, we have been moving with the room." Cube at this time is like a huge non-stop rotating Rubik's Cube, every time Each room is moving from time to time, and each coordinate only represents the location of the room at the beginning.
· The room moves
movement locus of each room is also hidden in the Cartesian coordinates of which, such as the coordinates 477, 804, 539 of the room, its Cartesian coordinates (18, 12, 17). To know the trajectory of this room, you can do this. For each three-digit number, do the following:
1. Hundreds digit minus tens digit
2. Tens digit minus single digit
3. Single digit minus hundreds digit
of three digits are the above operations, namely:
1. 477:. 4 - = -3. 7 | 7-7 of = 0 | = 7-4. 3
2. 804:. 8 - 0. 8 = | 0-4 =-4 | 4-8=-4
3. 539:5-3=2 | 3-9=-6 |9-5=4 In
this way, three vectors (- 3, 8, 2), (0,-4,-6) and (3 ,-4, 4). These three vectors represent the moving trajectory of the room. The coordinates (which can be regarded as vectors) that represent the initial position of the room converted into rectangular coordinates are added to these three vectors in turn, namely:
(18, 12, 17) + (- 3, 8, 2) = (15, 20, 19)
(15, 20, 19) + (0,-4,-6) = (15, 16, 13)
(15, 16, 13) + (3, -4, 4) = (18, 12, 17) It
can be seen that after three changes, it returns to the original initial coordinates (18, 12, 17). Each room is based on this rule to (18, 12, 17) --> (15, 20, 19) --> (15, 16, 13) --> (18, 12, 17) -->… The trajectory is moving.
· The change in position over time of the room
according to changes in the coordinates of the displayed, in fact, each room in the cycle moving in a fixed path. If you want to know the location of the space, you must also have a reference, that is, you must know the coordinates of at least one neighboring room. For example:
the room with coordinates 320, 176, 223 (recorded as room 1), the rectangular coordinates are (5, 14, 7), with (5, 14, 7) --> (6, 8, 7) --> (8, 9, 6) --> (5, 14, 7) -->... moves
the room 214, 168, 104 to the right of it (recorded as room 2), the rectangular coordinates are (7, 15, 5) , Move with (7, 15, 5) --> (8, 10, 6) --> (5, 8, 2) --> (7, 15, 5) -->...
The rooms 254, 303, 017 above it (denoted as room 3), the rectangular coordinates are (11, 6, 8), with (11, 6, 8) --> (8, 9, 7) --> (9 , 6, 1) -> (11, 6, 8) -> ... the trajectory
from the respective three mobile three rooms can be seen they are not always adjacent, in other words, only when When room 1 arrives (8, 9, 6) and room 2 arrives (8, 10, 6), they are adjacent to each other, and only when room 1 arrives (8, 9, 6) and room 3 arrives (8, 9, 6). , 9, 7) When the two are next to each other, the 3 rooms are separated from each other during other times. Not all rooms move together at the same time, but their movements are independent of each other. In this way, the Cube has an initial state. At this time, all the rooms stay on their initial coordinates. After that, the rooms will move individually and return to the initial state after a certain period of time. This cycle may take several days, depending on The size of the cube, which will also affect the time required to reach the "bridge".
· "Bridge" and exit
"Bridge" are actually a room, as mentioned above, in its initial position it connects the shell and the inner big cube, and the exit is inside the "bridge". The Y-axis coordinate of "Bridge" is 27, and the Y-axis coordinates of other rooms are not greater than 26. The "bridge" also moves on a fixed trajectory like other rooms, which means that it is only a real "bridge" when it reaches its initial position, and people can walk out of the Cube through it, and it stays in the big cube at other times. For other positions inside, you must seize the timing, and wait for another round of cycles after missing the initial position. Leaven compares Cube to the lock of a safe. The lock can only be opened when all the rooms reach their initial position, but then as soon as the room moves, the lock is closed. Therefore, if you want to find the exit, you must first find a room on the boundary surface of the big cube (a certain coordinate is 26), then select the room along the boundary to enter, and finally find the "bridge", and then wait for it to return to the initial position before you can get out of the Cube. .
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I pretended to be very interested and read it again. As a result, because my young mathematics skills are on the same level as the Indian flying cake, I am looking forward to something like a "professor of the Department of Mathematics of Massachusetts Institute of Technology"...囧rz...
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