On the Subject of Piragua

Hey pana, I run this town!

• This module contains a cup of unflavored piragua, and a bottle of syrup. To solve the module, pick the correct flavor. Pressing the bottle changes the flavor in it, which can be identified by the color of the syrup, and pressing the piragua submits.
• Follow the instructions below to calculate two numbers, A and B. These will provide a final solution digit which corresponds to the correct flavor.
• If A and B are coprime, the final digit is the digital root of the sum of A and B.
• If A and B are not coprime, the final digit is their greatest common denominator, modulo 10.
• Every time a Piragua module solves, the final digit to every other Piragua on the bomb increments by one (modulo 10 if necessary).

Calculating number A:

• Concatenate the following numbers to create one bigger number:
  • Number of batteries
  • Number of ports
  • Number of indicators
  • Number of modules (including needies)
  • Starting time in minutes
• Go through the number and remove any digit that has already occurred.
• Multiply the resulting number by the number of battery holders times the number of port plates, plus 1.
• This product modulo 10,000 is number A.

Calculating number B:

• Calculate 4 digits using the following instructions.
• The first digit is the number of modules on the bomb containing “arrow”, “identification”, or “simon”.
• The second digit is the day of the week on which the bomb was started, with Sunday being 1.

• Consider a port plate with a parallel or serial port on it to be type 1, and a port plate with any other port on it to be type 2.
  • If type 1 and type 2 are present, the third digit is 1.
  • If only type 1 is present, the third digit is 2.
  • If only type 2 is present, the third digit is 3.
  • If neither type is present, the third digit is 4.
• If the first digit of the serial number is even, add 5 to the third digit.
• The fourth digit is the last digit of the serial number.
• Create a 16-digit number by repeating these digits 4 times. Divide the result by 17. There will never be a remainder.
• This result modulo 10,000 is number B.

Syrup flavors:

Note that viewing the syrups through the plastic bottle changes their coloring slightly, but they are still distinct.

	China (0)		Uva (5)
	Melao (1)		Anis (6)
	Fresa (2)		Frambuesa (7)
	Limón (3)		Ajonjolí (8)
	Guanábana (4)		Tamarindo (9)