"What took you so long? I've been standing here for the last 10 minutes!" he said as he walked past him and entered the house.
"Yes. You can come in." said Balram closing the door.
"I think you're becoming deaf. If you hadn't opened the door now, I swear I would have banged on the door."
"Did it occur to you, that it was quite possible, that I wouldn't be at home? It's a Sunday and people have weekend plans."
"You want me to think that, don't you? You have a problem with me barging in like this?"
"Now I don't have a choice, do I?"
"Yeah. You don't. Is that coffee you're drinking? Can I have it?"
"No. I'll make another cup of coffee for you."
"Thank you. Make it a bit strong. And don't be stingy with sugar."
"I see. So what makes you so impatient today?" asked Balram as he went into his kitchen.
"Ah! Don't ask!" said Suyodhana following him.
"I already did. And I have a feeling you want to talk about something."
"Rishi was at home this morning. The kid wanted me to teach him mathematics. GCD, LCM and what not! I just spent more than an hour trying to put some sense into that boy. But the boy! Oh boy! Nothing gets into his head! It's such a simple thing -- Greatest Common Divisor, Least Common Multiple. It's not like only the greatest can understand it. He doesn't put the least effort in understanding it either. Keeps confusing between the two. And if I scold him, he talks back! Oh the boy has some guts, I tell you! He asks me what use it is to learn such stuff! Can you imagine how difficult it is to deal with such kids?!" said the exasperated Suyodhana.
"I can only imagine." said Balram with a hint of a smirk passing his face. "So were you successful in teaching him?"
"I was able to help him solve his homework. But that boy is dumb. He'll forget it before his exams."
"So you weren't successful?"
"Bah! Who cares!"
"Why did you agree to teaching him mathematics? That too so early on a Sunday? It's quite strange."
said Balram, as he handed the strong coffee with extra sugar to Suyodhana. They started walking back towards the balcony.
"His mom asked my mom. I couldn't refuse."
"Interesting."
"Why is that?"
"Doesn't Rishi have an elder sister? She is your age isn't she?"
Suyodhana blushed for a second before changing his expression, "Oh! How sly of you! You think I'd do anything like that just to get in the good books of his sister?!"
"Wouldn't you?"
"Would you?"
"This is about you, not me." said Balram looking at Suyodhana with a raised eyebrow and a mocking smile. Suyodhana kept silent and sipped the coffee. "So, were you able to tell Rishi about the practical uses of GCD & LCM?" he asked.
"I told him some things I got off the Internet."
"What are they?"
"Oh, you don't know either? You want me to teach them to you too?!"
"Yes. Please do."
"OK! I give up. I don't want to make a fool of myself in front of you. I seriously can't understand the real uses of these things. These and even Prime Numbers. God! Why do people make so much noise out of it, is beyond me!"
"I think a story needs to be created to make this interesting. A hypothetical situation."
"I'm all ears." said Suyodhana, getting comfortable and leaning back in his chair. "Why else do you think I'm here?!"
"Alright. Do you see Giridhar leaving his home there? He has taken money from some Chaturvedi and hasn't repaid him. Chaturvedi doesn't know where Giridhar lives, but they go to work from the same bus stop. Now here is the hypothetical problem.
1. Chaturvedi (C) and Giridhar (G) leave their home only once a day. We'll assume it's the same time of day too.
2. If C meets G, G has to pay whatever money he has. Or he runs the chance of being humiliated in front of others; or worse being beaten up.
3. Both can't stay at home for very long. G works as a researcher who does most of his work from home and doesn't have to go to office regularly. C is a writer who goes out occassionally to meet people.
"Now, if C & G met daily, G would have to pay every day and he wouldn't save anything for himself. So, he decides to go out once in 2 days. C realises he meets G on alternate days & he changes his schedule too. G changes his schedule to 3 days now. When will C & G meet now?"
"Umm. Every 6th day? Ah. I see that's the LCM of 2 and 3!" said Suyodhana.
"Yes. Now, G doesn't have enough money to give every 6th day either and he has to change his plans. If he goes out every 4 days, he'll run in to C every time he went out. Same goes with every 6 days and so on. You understand why it is so?"
"Because 2 is a prime and those numbers are its multiples?"
"Precisely. So our researcher G decides to go out only on prime number intervals. C keeps altering his schedule too to grab hold of G. If G came out every 7 days & C came out every 5 days, G gets 35 days to collect sufficient money for the month. G tries to increase his gaps and not finding him often, C reduces his gap. G can't be at home for long periods; he has to go out to get work and money. C can reduce his gap to every day, but he gets frustrated at not finding G often. The question that arises is 'What is the optimal gap for each of them?'"
"I get it! C has to choose a small prime number - a greatest common divisor. While G has to choose a reasonably high prime number so that their least common multiple is big enough for him to have enough money for him." said Suyodhana with a tinge of delight in his voice.
"Yes. That's correct." said Balram who was glad that Suyodhana understood the problem.
"Wow! That's cool!"
"The problem is a type of Predator-Prey model. And this particular solution is called Predator Satiation. It is often seen among cicadas. They appear once in 11 or 13 years in large numbers. It's a type of evolutionary adaptation process that allows them to survive assaults from their predators. There are many other uses of Prime numbers, but very few like these can be spotted in nature. You can see uses of Primes in encryption algorithms like RSA. There are many other applications of primes too, but I'd rather have you discover them."
"No, no. That's ok. This is sufficient. Now, if only I could make that kid understand all of this!"
"Or, from what I have gathered, more importantly, you should attempt to tell him that with his sister around."




