# Computer Puzzle - Arithmetic Of The Day

Harou, a Japanese teacher in the school, noticed a ship made of paper outside her office.
When she unfolds the paper, she saw something strange.
There is something that looks like a riddle, followed by some weird arithmetic lines.

Riddle:

My prefix is something that controls you.
My suffix is something that students mustn't do.
My infix is one over nothing.
My whole is the key to the lines below.

Code:

(1) $$82+1.13-1.1-1.1>32+1.1<19+1.15-1.1+1.11+1.15-1.1>1.1<14+1.3-1.4-1.3-1.11+1.$$
(2) $$70+1.6+1.11-1.6+1.1>32+1.1<14+1.2-1.14-1.1-1.1>1.1<5+1.5+1.1>1.1<5+1.14-1.8+1.12-1.15+1.8-1.7+1.3+1.13-1.$$
(3) $$70+1.9+1.6+1.3-1.1>32+1.1<15-1.2>79+1.2<9+1.2>1.2<6+1.1>1.1<1+1.2-1.4+1.20-1.17+1.13-1.$$
(4) $$70+1.6+1.3-1.7+1.1>32+1.1<4+1.5-1.1+1.1>1.1<1-1.9-1.1>1.1>49+1.$$
(5) $$83+1.16-1.12+1.5+1.8-1.11-1.13+1.10-1.$$
(6) $$65+1.1>32+1.1<17+1.3-1.6+1.7-1.10-1.1>1.1<12+1.11-1.2+1.1>1.1<2+1.5+1.1>1.33+1.33-1.1<5+1.2-1.3+1+1.20-1.17+1.13-1.1>1.1<3+1.7+1.3-1.7-1.$$

Question: Find the hidden six-letter word.

This may be hard.

Hint 1:

Why did the student fold the paper into a ship?

Hint 2:

The $$<$$ and $$>$$ are not self-defined operators.

Hint 3:

The riddle reveals a programming language.

Hint 4:

You can use this one to raise things:
$$1,10-1[22-1.1,10-1]$$

Hint 5:

All the numbers matter.

Hint 6:

$$70+1.3+1.13+1.17-1.1>32+1.1<2-1.15+1.3-1.4+2.14-1.14+1.$$ makes 0.

Hint 7:

Notice that the tag is missing.

warning: spoilers contain profanity

Brainfuck

My prefix is something that controls you

My suffix is something that students mustn't do

f*ck: Students (especially high-school/lower-school ones) should not f*ck (have sex)

My infix is one over nothing

inf: this is a shorted version of infinity, or the result of dividing 1 by 0

And it's a programming language, as noted by a hint

I have no idea how to go fro here.

Partial Answer (almost done; can't figure out the last part)

Warning: The design of this puzzle pretty much requires some mild profanity, so consider yourself warned.

# Riddle

Note: I'd already figured this part out before @bobble posted her answer.

Looking at the code, I recognized it as

based on the programming language called "Brainfuck."

Looking at the riddle,

My prefix is something that controls you.

The prefix is "brain," which is also the name of what controls us.

My suffix is something that students mustn't do.

The suffix is "fuck," which, of course, students shouldn't do.

My infix is one over nothing.

The infix is "inf." $$\frac{1}{0}$$ (one over nothing) is sometimes said to represent infinity, which is often abbreviated "inf." More formally, $$\lim_{n\to 0^+}{\frac{1}{n}}\to\infty$$

My whole is the key to the lines below.

The whole, "Brainfuck," is the name of the programming language for the code.

# Code

Brainfuck only has the following characters: ><+-.,[]. You can read more about these commands on Wikipedia. To summarize them, > and < move the data pointer one cell right or left, respectively. + and - respectively increment and decrement the data at the pointer. It does not have numbers, so I had to figure out what the numbers were for.

# Numbers‽

My first guess was that a number meant to add that number. That was wrong. My next guess was that a digit meant to add that number. Also wrong. Then, I noticed that it alternated between numbers and commands, so I decided that the numbers probably meant to run the following command that many times. This turned out to make sense.

## Decoding

I tried using Hint 6 as a "practice run" to see if I was right. I noticed that each . was preceded by a 1 most of the time, with the 2. corresponding to what I hoped was merely a double letter. This gave me more confidence. Using the value at the pointer for each output command as the ASCII value for a character, Hint 6 says "FIVE CROSSES" makes 0. At this point I didn't know what that meant, but I knew "FIVE CROSSES" was definitely not gibberish. (I'll explain this later at the point in the process that I figured it out.)

Using the principles I used to decode Hint 6, the 6 ASCII-encoded messages are:
(1) 82 69 68 32 87 72 73 84 69 32 83 80 76 73 84
(2) 70 76 65 71 32 85 83 69 68 32 73 78 32 83 69 77 65 80 72 79 82 69
(3) 70 79 85 82 32 67 79 76 79 82 32 83 81 85 65 82 69
(4) 70 76 73 80 32 84 79 80 32 79 70 32 49
(5) 83 67 79 84 76 65 78 68
(6) 65 32 82 79 85 78 68 32 80 69 71 32 73 78 32 65 32 83 81 85 65 82 69 32 72 79 76 69

Converting these numbers to text, the messages/clues read:

(1) RED WHITE SPLIT
(2) FLAG USED IN SEMAPHORE
(3) FOUR COLOR SQUARE
(4) FLIP TOP OF 1
(5) SCOTLAND
(6) A ROUND PEG IN A SQUARE HOLE

These clues each correspond to a signal flag as follows:
(1) ? (RED WHITE SPLIT)
(2) O (FLAG USED IN SEMAPHORE)
(3) ? (FOUR COLOR SQUARE)
(4) ? (FLIP TOP OF 1)
(5) M (SCOTLAND)
(6) ? (A ROUND PEG IN A SQUARE HOLE)
To figure out which system to use for the numeral 1, I noticed that five crosses makes 0 in the U.S. Navy only. (This is when I finally understood Hint 6.)

This is the farthest I got. I've gotten past all the hints, but I'm stuck.