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Structure[]

The cube is comprised of 26 x 26 x 26 rooms, plus 1 bridge room, making up 17,577 total rooms. The outer shell is 434 feet on one edge or 81,746,504 cubic feet, with a single door.

Coordinates[]

Each room has a serial number consisting of three numbers, each three digits. The sum of the digits in the number represent the x, y and z coordinates of the room's starting position in the whole cube. It is important to note that every sequence of 3 digit numbers can be represented in the 17,576 (26 cubed) rooms without the possibility of overlapping the available Cartesian coordinates derived by adding the digits in the serial numbers. Since there can only be 78 (3 x 26) instances of any given x, y or z value, and 14 is the mode value of the sums of digits for numbers between 001 and 999, with a count of 75 occurrences, then any unique set of 3 digit numbers can be used. The bridge room has a coordinate of 14, 27, 14 which brings the count to 77.

Traps[]

Trap rooms have at least one of the serial numbers as a power of a prime. Originally, Leaven thought that prime numbered rooms were the only traps, making a potential 459 (153 prime numbers between 2 and 991 multiplied by 3 potential coordinate values) trapped rooms. Since a prime number to the power of 1 is also prime, it is easy to understand her mistake. However, there are 25 non-prime powers of primes below 999:

4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961

This makes a potential total of 534 trapped rooms based on the power of prime rule.

Moving Rooms[]

The rooms move at regular intervals in a set sequence. Leaven compares it to a big combination lock. The permutations of how the rooms move can be found by subtracting the digits in each of the serial numbers.

The bridge room has a Y coordinate of 27, which has a Y serial number of 999, making its Y movement value 0. This means it will always stay within the same vertical plane of Y:27 according to the movement rules, essentially sticking to one side of the outer shell. This creates a potential plot-hole since the first time they are in the bridge room they were able to pass "through" it. If the movement rule hold true to the bridge room, then there can only be one tunnel that can enter the room, one tunnel facing the inner-wall of the shell or the door, and the other 4 into empty space.

When the movement happens and how often is not explained in the film.

Full example[]

Suppose a room has the serial number 242 614 064 (not shown in the film). The room has the starting position X:8, Y:11, Z:10. It is not a trap room, as no number is the power of a prime, and will move X:-4, Y:1, Z:2 during its movement.

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