## On the Subject of Functions

I know exactly how to get 8 from 1 and 3!

Type “5,8478” and query and find the result in the following list. This tells you which function is in use.

1 2 483 808 1010 23 #10 #19 #4 #28 #27 #31 #3 #29 #36 #20 #38 #2 #21 #30 #24 #37 #18 #17 #7 #22 #41 #14 #13 #39 #11 #34 #0 #12 #32 #23 #35 #26 #40 #16 #5 #33 #8 #1 #6 #25 #9 #15
• Use additional queries to differentiate functions #9 and #15 from the others if necessary.
• Use the letter on the bottom row along with Table 2, finding an offset to apply to the function number, to find your final function. Wrap around as necessary.
• Submit the answer to the final function using the bottom displays as input.
• If the answer is empty, submit 0 instead.

### Table 1: Functions

 #0: Digital root of ((a+b) squared) #1: a*b, even-positioned digits removed #2: 8, then number of odd digits, then number of even digits #3: Digital root of (a+b) #4: (a+b) modulo 1000 #5: (a+b) squared #6: Highest digit #7: 10 - number of distinct digits #8: (Larger*2) - Smaller #9: Sum of times each digit appears in serial number #10: Number of even numbers #11: Dots found in digits when using morse code #12: a+b, concatenated with |a-b| #13: floor(larger / smaller) modulo 1000 #14: Digital root of |a-b| #15: Lit indicators times 63 #16: a*b #17: (a*b) modulo 1000 #18: (sum of a's digits) * (sum of b's digits) #19: smaller - (larger modulo smaller) #20: a*b, odd-positioned digits removed #21: All digits missing from the number string 1234567890 #22: Lunar Addition #23: a*b, odd digits removed #24: (Digit, then 2 if even and 1 if odd) for all distinct digits in order #25: floor(sqrt(a) + sqrt(b)) #26: Digital root of (a*b) #27: Number of digits times 202 #28: 808 #29: 810 - (Number of variables below 100) #30: Larger modulo smaller #31: Sum of letters in each English-written digit #32: (Product of first and last digit of a) * (Product of first and last digit of b) #33: floor(sqrt(a+b)) #34: Product of first and last digits overall #35: a squared + b squared #36: (a+b) modulo 12 #37: |a-b| #38: (Digit concatenated with the number of times that digit appears) for all distinct digits in order #39: a+b #40: floor(larger / smaller) #41: floor((a+b) * (larger / smaller))
Digital Root: Sum of digits until a single digit is obtained. D.R. of 129 is 3.
Modulo: The remainder from a division problem. 10 modulo 3 is 1.
Absolute Value or |x|: The difference of x and 0. |2-6| = 4.
sqrt(x): Square root. sqrt(9) = 3.
floor(x): Round down.
Squared: Multiplied by itself. 5 squared is 25.
Lunar Addition: Addition but in each place, take the higher number instead of adding. In Lunar Addition, 184+229 = 289.

### Table 2: Letter Adjustments

ConditionTrueFalse
A: KBU or M in SN?+6-4
B: Battery, indicator, or port count = 2?+2-3
C: First character in SN a digit?+5-4
D: Lit BOB indicator?+8-8
E: Unlit BOB indicator?+6-2
F: First character in SN a letter?+6-5
G: Parallel port but no Serial port?+1-5
H: At least one empty port plate?+1-3
I: No batteries?+1+5
J: Vowel in SN?+5-3
K: Indicators > 3?+4-1
L: Battery count even?+6+7
M: Ports > indicators?+3-7
N: More lit than unlit indicators?+3-5
O: Indicators > batteries?+6-1
P: Indicator count even?+2-3
Q: ERI or S in SN?+1-3
R: Exactly 3 letters in SN?+3-2
S: Batteries > ports?+2+4
T: Batteries > 4?+4+1
U: Lit and unlit indicator count equal?+2-2
V: JQX or Z in SN?+7+1
W: At least three ports?+3-5
X: No indicators?+3-3
Y: 4+ SN digits?+4-1
Z: No ports?+5-1