## On the Subject of Black Holes

Ground control to Major Tom, do you read?

• To disarm all Black Hole modules on a bomb, obtain a code consisting of digits 0–4. The length of the code is 7 times the total number of Black Hole modules on the same bomb. At any point, you may enter the next digit of the code on any unsolved Black Hole module.
• If you solve a different module on the bomb after entering a digit of the code, the code gets shortened by two digits, except when your digit caused a Black Hole module to become solved. This way the code for a single Black Hole can be reduced from 7 to 3 digits by solving other modules between entering digits. The code for two Black Holes can be shortened from 14 to 6, etc.
• Observe the 10×10 grid on the next page. Calculate your starting location in this grid from the bomb’s serial number. The third character is the x-coordinate, the sixth character the y-coordinate. Columns and rows are counted left-to-right/top-to-bottom from 0.
• To determine your initial direction of movement, start by facing north, then turn 45° clockwise for each port on the bomb.
• Obtain the first digit of the code from that grid location, then move one space in your initial direction, then rotate your direction 45° clockwise.
• The next digit is the sum, modulo 5*, of two consecutive grid locations in your current direction. Obtain the two numbers, move one space beyond them, then rotate 45° clockwise.
• Proceed likewise for every subsequent digit, adding one more grid location each time. The nth digit of the code is the sum (modulo 5*) of n consecutive grid locations.
• Every time you move beyond the edge of the grid, wrap around to the opposite side.
• The following page explains the gesture for entering each digit.
• The “C” gesture can be used to determine how many correct digits have already been entered in case you lost track.

* “modulo 5”: Add/subtract 5 until the number is in the range 0–4.

• In the above diagrams, a dot represents a tick of the bomb’s countdown timer (i.e., a change in the seconds value) going from left to right.
• A vertical line represents a tap on the module. Make sure that you press and release the module between two ticks.
• A bracket indicates holding the module across one or more ticks.
 3 4 1 0 2 3 1 2 0 4 1 3 0 2 4 1 2 3 4 0 3 2 4 2 1 3 0 0 1 4 4 0 0 1 3 4 2 2 1 3 1 2 1 3 0 0 4 3 4 2 4 0 2 3 4 1 3 0 2 1 2 1 3 1 3 0 4 4 0 2 2 4 4 0 0 2 1 1 3 3 0 1 3 4 2 2 0 4 3 1 0 3 2 4 1 4 3 1 2 0