Without the probabilities, it’s hard to calculate its efficiency. But ultimately, there’s only two choices, reinvest the eggs or sell them. So fundamentally, it’s no different from the [Wood Minion].

“So, what do you think about it, Sumire?”

“I’d like to wait a little longer to at least gauge how likely each animal is.”

Suddenly, we received a notification on our phones again.

-

From: TAG Administration

You should all have started to settle in to your new schooling. Classes will be introduced tomorrow, these will teach a variety of subjects from English to Math to Science. They will be directly relevant to ‘Surprise Questions’ and also school exams. It is highly recommended but not compulsory.

Classes will be held in the lecture halls on floors denoted below. You may attend any class you wish at any time. Classes will run from 8am to 8pm every day.

Math Classes: Floor 25

English Classes: Floor 50

Science Classes (Biology, Chemistry, Physics, Psychology, Environmental Sciences): Floor 75

Humanities Classes (History, Geography, Social Studies): Floor 100

Other Classes (Physical Education, Art, Music): Floor 125

-

“I guess this is supposed to be a school, after all.”

“Are you going to attend any classes, Akira?”

“I might if I don’t have anything else to do.”

It’d be a decent way to pass the time.

However, the school wasn’t done with its communication. Like an insecure girlfriend, a second message came through in due time. This time, the announcement was just as profound as the last.

-

From: TAG Administration

Violence is strictly prohibited within the school. Anyone caught will face severe consequences. The DUEL App has been unlocked for the purpose of challenging students to physical battles.

The app will allow you to challenge any student to a duel—wherein you fight in an arena which all physical harm is simulated. Other conditions are variable and can be seen on the app.

-

“Do you want to duel, Akira?”

“Not particularly. There’s not much to be gained for either of us, is there?”

“But don’t you just want to try it out for fun?”

Not really.

POINTS

Your current points: 2,159

Current Rank: #81,199

I decided to have a look at the DUEL app, just to see what specifics it entailed. There were a few different options in terms of consequences. You could duel with the loser facing {Expulsion}, you could duel for Points and you could duel with a custom set condition at the end.

However, the most interesting one seemed to be something called a {Rank Challenge}. It was the only option which allowed you to force your opponent to accept the duel. All other duels were optional for the one being challenged.

It had a condition relating to ‘Castes’, which would likely be revealed later.

Surprise Question

Let Z≥0 be the set of non-negative integers, and let f : Z≥0 x Z≥0 → Z≥0 be a bijection such that whenever f(x1, y1) ≠ f(x2, y2), we have f(x1 + 1, y1) ≠ f(x2 + 1, y2) and f(x1, y1 + 1) ≠ f(x2, y2 + 1). Let N be the number of pairs of integers (x, y), with 0 ≤ x, y < 100, such that f(x, y) is odd. Find the smallest and largest possible values of N.

Write your answer here: _________________

It seemed that they upped the difficulty a little with this question.

I looked over at Sumire, who appeared to be scratching some little markings in my table with her nails. It wasn’t anything too noticeably but it was certainly not a nice thing to do.

I didn’t see why she needed to make markings anyways.

Well, to be fair, I had seen this exact questions before on a set of olympiad questions we were given a few years ago, so I already knew the answer—not that I really needed it. The answer was also much simpler, meaning I didn’t have to struggle with the undersized phone keyboard.

Correct!

You were the #1^st  student to answer that correctly. (3.19s elapsed)

You have been awarded 5,000 points

Whilst time was the main variable for Sumire and I, I did notice that the difficulty had been increased significantly. For students who couldn’t answer the previous questions, this question would be completely impossible.

Regardless, I guess this was a meritocracy after all.

I’m surprised I got first.

Sumire laughed a little as she typed the answer to the question on her phone.

“You’re finally showing what you can do, Akira.”

“I just answered the question like all the ones before.”

“You were faster than me this time.”

///

…

Ow.

What was that? It was like a life of memories flashed through my mind.

—It’s always like that.

Who was that?

“Are you okay? You’re staring into space again, Akira.”

“Yeah, I’m fine. My head just hurt for a moment.”

“Just out of nowhere?”

“Yeah. I don’t know what that was. Maybe it’s because I’m hungry.”

Sumire lowered her phones, still tapping it with her thumb. Hopping off the table again, she walked over to me.

“Well, we’ve got 10,000 more points now between the two of us, don’t we, Akira?”

“I guess so.”

“You want to have a meal?”

“I guess I am a bit hungry.”

“We can share something. I don’t need to eat that much.”

We’d probably done a few too many laps of the place, but such was the consequence of the spontaneousness of our point acquisition. It wasn’t like we necessarily had anything to do at the moment. She transferred all her points to me.

“Just take half of what you spend and send back the rest, Akira.”

Sumire’s footsteps echoed through the room as she walked to the door again.

*

“There’s this salad meal here that’s a bit cheaper, do you want to get that?”

Sumire standing a few metres away since there were way too many people all crowding in front of the restaurant. I wasn’t sure if she heard my voice through all the chatter, but I’m sure she could extrapolate what I meant.

I didn’t hear what she said in response but she gave a thumbs up.

With that, I slowly pushed my way through and ordered a meal.

Large Caesar Salad—8.5k points