 ## On the Subject of Arithmelogic

(Math is fun) ⊻ (Bomb is armed) = True.

• This module contains a submit button with a symbol on it, three pressable displays with four numbers each, and a display showing a three-element logical statement.
• Each of the symbols within the three-element logic statement corresponds to a certain value, as shown on Table A.
• The submit button has a symbol that corresponds to a condition, also on Table A. Numbers that meet that condition are considered TRUE, others are considered FALSE.
• You can cycle through each display’s numbers by pressing that display. At least one of the numbers in each display, when added to the associated symbol’s value, will make that element true, and at least one will make it false. To submit an answer, press the submit button.
• IMPORTANT: When submitting, the symbol’s value for an element will be added to the number in the screen above it before the three-element statement is evaluated. The parenthetical statement will be evaluated first.
• If, when submitting, the statement as a whole evaluates to true AND, for each final calculated element within the three-element statement, there is no higher number for that button’s display which would keep the true/false value of that element the same, the module will be disarmed. Otherwise, a strike will be given.

### Table A: Symbols and their meanings

Symbol Value if in statement Condition if submit button
© The submit symbol’s position in the manual’s table The number is even
Ѯ The earliest position of serial number letters in the English alphabet The number is a multiple of 7 or 13
The average serial number digit, rounded up The number modulo 3 = 1
Җ The number of indicators The number is prime
Ѭ The number of battery holders Any of the number’s digits are odd
Triple the number of lit indicators The number modulo 5 = 2 or 4
Ϡ The day of the month when the bomb was activated The number’s digits add up to a number from 9 to 13, inclusive
Ѧ The lowest serial number digit plus five The number’s last two digits are within two of each other
æ The total number of ports The number modulo 7 = 1, 3, or 6
Ԇ The number of unlit indicators times four The number contains a 3 or 6
ϫ The number of serial number consonants times five The number’s digital root is odd

### Table A cont’d

Symbol Value if in statement Condition if submit button
Ӭ The number of batteries The number is a multiple of 4
Ͼ The sum of the serial number’s digits The number’s digits add up to an odd number
Ѫ The latest position of serial number letters in the English alphabet The number is odd
Ҩ The total number of modules on bomb modulo 25 The number’s digits don’t add up to a number from 7 to 11, inclusive
Ϙ The number of serial number vowels times six The number is a multiple of 6
ζ The number of batteries plus indicators The number’s digital root is even
Ͽ The number of lit indicators plus port plates The number is composite
ƛ The number of port plates The number’s digits add up to an even number
The highest serial number digit The number contains a 2 or 9
Fifteen The number modulo 4 = 1
œ The number of unlit indicators plus battery holders The number’s last two digits are at least five apart

## Appendix of Things to Know

### Logical Connective Symbol List

Logical Connective Symbol Logic Gate Equivalent Meaning
Conjunction AND Returns true if all inputs are true. Else returns false.
Disjunction OR Returns true if any input is true. Else returns false.
Exclusive Disjunction XOR Returns true if exactly one input is true. Else returns false.
Alternative Denial | NAND Returns false if all inputs are true. Else returns true.
Joint Denial NOR Returns false if any input is true. Else returns true.
Biconditional XNOR Returns false if exactly one input is true. Else returns true.
Implication (Left) - Returns false when left input is true and right input is false. Else returns true.
Implication (Right) - Returns false when left input is false and right input is true. Else returns true.
• Modulo is the remainder from a division problem; 10 modulo 3 is 1.
• The digital root is the continual summing of a number’s digits until the result is a single digit number from 0 to 9.
• Vowels are A, E, I, O, and U.
• Prime numbers from 2 to 200 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199. If your number is greater than 200, the first thousand prime numbers can be found here. Composite integers are integers greater than 3 and not prime.