Before the start of the tournament with the branches, a teacher explained how it would work.
The teacher stepped onto the stage, where there were two tables on either side, each with a notebook and a button — one red and the other blue.
—Alright, here is how the tournament will go. You will compete one-on-one. Questions or equations will be given, which you must solve, and you will have 3 minutes to do so. The first one to solve it must press the button and state their answer. If the answer is correct, you earn a point. The first to reach ten points wins and moves on to the next round.
Dan and Jack looked at each other at the same time; both were determined to reach the final and win. Standing between them was Noemí, trying to calm her nerves.
—Very well, let us begin. The first participants will be... Dan and Cristofer.
Dan walked onto the stage at the same time as Cristofer, the latter looking far more confident than Dan.
The teacher stood in the middle of the two, holding a sheet of paper in one hand and gripping a microphone with the other.
Noemí whispered.
—Good luck.
The teacher began to speak.
—Here, the fastest one wins. What is the equation of the line with a slope of –2 that passes through the point (1,3)?
Dan pressed the button the moment the teacher finished the question.
—y = -2x + 5
—Alright, very good. Point to Dan.
Dan's score went up from 0 to 1. He turned to look at Jack with confidence. Jack rolled his eyes.
—Second question. Solve:
5x - 9 ≤ 16
Dan pressed the button again. Cristofer started to get annoyed; when it came to reaction speed, Dan was faster.
—x ≤ 5
—Correct. Point to Dan.
The round continued, and Dan managed to reach ten points without a single wrong answer. Cristofer was unable to respond to any question.
Dan stood up from his seat and stepped down from the stage, wearing a wide smile.
—Congratulations, Dan.—Said the teacher who was accompanying them.
Jack looked away, crossing his arms.
—Yeah, that was luck.
Dan frowned.
—Sure, you call it luck so you don't have to admit I'm better.
—I most certainly do not.
—Congratulations on moving on, Dan.—Said Noemí happily.
He blushed slightly.
—Thanks... I hope you can pass too.
The teacher announced the next round, in which Jack would take part.
—I can do the exact same thing, Dan.—He walked toward the stage.
Every word made Dan more frustrated. Just as he had said, Jack also won with a perfect ten points. He stepped down from the stage and walked over to them.
—What did you think?
Dan huffed, and Noemí smiled.
—Congratulations to you too, Jack.
—Thanks, Noemí.
The following rounds moved forward. Noemí's turn arrived; she was nervous, but she walked up onto the stage.
Dan gave her two thumbs up.
—Good luck, Noemí.
Jack smiled and nodded his head, wishing her luck as well. She turned to look at them with a smile, grateful for their support.
Noemí managed to pass, earning her ten points, though with some difficulty. She came down from the stage and walked back toward them.
Jack was happy for her.
—Congratulations.
—Thank y...
Before she could finish thanking him, Jack placed his hand on top of Noemí's head and patted her. She stood still, unsure of what to do.
It took Dan a moment to process what was happening, but when he did, just seeing it gave him a strange feeling. His stomach felt like it was twisting, and his hand lifted up on its own.
Noemí turned her head to look at him, as did Jack. His hand was suspended in mid-air.
—Umm... I think we should get ready for the next rounds... Don't you think?
Noemí nodded with a smile and stepped away slightly to go speak with the teacher and ask about something she was unsure of.
Dan looked straight at Jack, narrowing his eyes. Jack looked back at him, confused.
—What? I was just congratulating her.
The rounds kept going, but now, every time Noemí finished and moved on to the next stage, Dan was the first one to go over and congratulate her, and he always positioned himself between Noemí and Jack whenever the three of them were together.
In Noemí's next round, she was eliminated. Her opponent had reached ten points before she did, ending with a score of 10-7.
She stepped down from the stage looking somewhat sad and disappointed in herself. Dan smiled.
—Don't worry, you don't win every time.
The teacher nodded his head.
—Exactly, besides, you didn't do too badly.
Jack raised his thumb in support. Grateful, she smiled again.
—Thank you. I would have liked to keep going, but I trust that one of you will win.
Dan pointed a thumb at himself.
—You can trust me. I'll avenge you against the one who eliminated you.
She laughed softly.
—Then I trust that you will do it.
—Just make sure you don't lose too.—Said Jack.
—Of course I won't. And you better get ready, because we're almost at the final, the two of us.
The teacher announced Jack's next round, and he started walking toward the stage.
—Get ready? I'm the one who should be saying that, because I'm already prepared.
Both of them only needed one more round to reach the final.