I was watching the shooting from a distance. You must have heard of the film “Muthu” being directed by K.Balachander (he’s KB to us). KB was explaining the shot to my husband, but he seemed to be shaking his head in confusion, so I decided to have a look.
“Rajni, you cannot throw up a cigarette and catch it in your mouth this scene. Your father has just died. Your eyes are blinded by tears.”
“But I can do it even with my eyes closed,” he protested.
I wasn’t surprised. Nor was KB. We had seen him do it with his mouth closed too. But that, obviously, was not KB’s point.
“This character doesn’t even smoke, Rajni,” explained KB.
“Nor did I until I was seven. It isn’t too late for him to start now. It’s never too late!”
At this point, I really had to intrude before KB slapped my husband. His temper was legendary, and I had a sneaking suspicion Rajni had been slapped more than most other artists put together. The above conversation, I suppose, explains the reason.
“Darling, if you want to smoke, you can smoke after the shot.”
“No Lata, my fans love my smoking. They watch my movies to see my style of smoking. They are still trying to find out how I throw the cigarette and catch it in my mouth. If I don’t do it, they will start committing suicide.”
I had no real answer to that. Every fan of his was mad. Even madder than him. Some committed suicide when he decided to renounce films, some when he decided to divorce me and many when he promised not to enter politics. It took over an hour to convince him that there were other scenes in which to show his style, until he finally relented. I left him to his ‘histrionics’ and wandered about the sets.
That evening I found him in drawing room, with a frown on his face. I at first thought he was in deep thought, but immediately dismissed the impossibility. He was just worried.
“What’s bugging you, dear?”
“On Friday I have a fight, Lata.”
“Good. You like fighting scenes, so what’s the trouble?”
“I don’t know whom to hit first.”
That really got me. He’d made many weird statements to date, including becoming disciples of liquor, Ramakrishna Paramahamsa, Sai Baba, Raghavendra, Ayyappa and ‘moola’, but this one took me by surprise.
He went on. “I have to hit the villain last. I know that. But whom should I hit first? If I don’t get it right the first time, KB has threatened to make me pay for every retakes. I can’t pay for 60 cars per retake!”
I rapidly made some calculations to the tune of 1.5 crores, and decided that he could earn the money in a few days of politics. But nothing was going to make me mention that to him. “Why don’t you explain,” I said, trying to calm him.
“Vikram Dharma has made a very complicated climax. 60 cars are following my car into a wasteyard. Then I must break their cars. They get out and form a circle around me. I have to hit all of them one after another while in air. That is easy. But Dharma has insisted that that I hit every second or third person only. Every time I hit them, they will obviously fall down and die. But the villain must be the last person I fight. So whom must I start hitting so that I correctly end up with the villain last? I don’t even know if I have to hit every second or third person. He will tell me only tomorrow.”
I shook myself awake. Not that I had any interest, but I decided to at least follow the problem. Besides, it sounded very much like the first part of police and robbers, where we had to choose the policeman.
“There are 60 men around you….,” I started.
“No, no, no! There are 60 cars. There may be many more men!” he screamed.
Not unusual. He generally goes up to a hundred in most fights. “… and you must hit all of them. You must hit every alternate person, and the last one you hit should be the villain.”
“Wrong again. It may not be every alternate person. It may be every third, or every fourth, or anything. Dharma will tell me only tomorrow.”
That was a rather interesting problem. And from what I knew of my hubby, he had as much chance of solving a mathematical puzzle by himself as a cat had in catching its tail. I had to throw in a lifeline. Just then I recalled that my friend had recently returned from the US, and her daughter was doing her second year at IIT Madras. She had been singing great praises of her cousin, who was also at IIT, and I thought this might be just the kind of thing for an IIT brain.
“I know somebody who may be able to help you,” I cautiously put in. “He’s an IIT student…”
He paused. “What is an ITT?”
I closed my eyes and slowly counted to ten. “I just think he can tell you whom to hit,” I said, and walked away before he could get me angrier. Over dinner, he persisted. “You think this ITT man will tell me whom to start with? Can you fix up an appointment, then? Please Lata, it is very important. Otherwise KB will slap me again.”
Well, it wasn’t often he said ‘please’, so I relented and called Priya.
“Hello, Priya. Lata here. Could you put Anuja on the line please?”
I waited for her daughter to come on. “Hello aunty, Anuja here.”
“Anu dear, do you remember you were telling me about a cousin of yours who’s studying with you? You said he was brilliant and all that…”
“Yeah aunty. He’s the second in his branch. Very smart. What about him?”
“Rajni uncle has a problem in mathematics, dear. We were hoping this boy could help him. Can you give us his address?”
“Certainly, aunty. He is a great fan of uncle. Just walk into his room. He will be delighted. He thinks uncle is the greatest thing on earth. I can’t imagine his shock when he sees Rajni uncle face to face.”
Oh no! Not another fan! Still, I took down his hostel address and passed it over to my husband. But I insisted that I accompany him. Just in case.
Taking Anuja’s suggestion, we decided to walk into his room on Thursday evening at eight. (Not unlike a certain other person. Hint to crossword experts : Lord Shiva’s better half is in a Jumble – Ed). The door of #219, Alakananda hostel was closed, but a light was turned on inside, so we knocked. A chubby boy in a dirty T-shirt and Bermudas opened the door.
“Are you Anand?” I asked.
“Yes,” he said. And before I could put in a word, “My God! Rajnikanth! Is it really Rajnikanth or is it Bhalla’s photography trick?”
“Vanakkam,” my husband said, folding his hands. “Naan Manidhan, eh, Manidhan. May I come in?”
The lad was obviously too dazed to say anything, and just sat down. His room was rather messy, with clothes, papers and books strewn all over the room, and a stereo playing Baba Sehgal’s latest (c)rap loudly. Strangely, there was no picture of Rajnikanth in his room, thought Agassi seemed to be an apparent favourite.
“My husband has a problem that he wants you to solve,” I began. The statement served the dual purpose of my introduction. “The problem is somewhat mathematical. Anuja felt that you were the best and suggested that we contact you. Would you like to look at the problem?”
“Yes, would you?” piped in the superstar. “You have to tell me whom to hit.”
Before the boy got scared, I explained the problem to him. I wasn’t sure if I was getting through, though. Half the time he would look at Rajni and the rest of the time crease his forehead and eyebrows. At the end of it, he sat back in the chair while we stared at him and let Sehgal’s noise permeate the room. I wished he’d switch it off before he started explaining. But no such luck.
“Could you just repeat the problem,” the boy began, when his hero got into the act and roared “Indha Baasha oru tharava sonna, nooru tharava sonna mathri.” If this Baasha says it once, it is as if he has said it a hundred times. Fine, but I was the one who had explained the problem. Still, the lad’s eyes were filled with unadulterated devotion and admiration, so I decided to sit back and watch the show. Rajni then took out his cigarette and threw it up. Pity the ceiling fan was somewhat low. Instead of flying towards his mouth, it flashed across towards the stereo. I was full of hope, but the hero in the room darted across, dived, and landed on the other fan’s belly. I must confess to his credit, however, that the cigarette did land right in his mouth. “Idhu eppadi irukku?” (How is it?)
After some of the commotion had settled down, I went through the details slowly once again while Rajni sat down on the bed to do some meditation. The boy too leaned back and closed his eyes, and I was left to stare at them. Their hairstyles were similar, mainly because neither had much. But other than that, fan had done little to resemble mentor. I appreciated that. In a while, both of them opened their eyes.
“OK, the problem can be done,” he began. “Let’s call the number of people you hit before one falls down as c,” proposed Anand. That means you miss c-1 people for every hit.”
“I don’t miss them. They are just not supposed to fall down,” protested the superstar. “I tried telling KB that with my image, even without me hitting them the should fall down, but KB said no. He said it was in some table.”
“The error function table,” declared Anand. “Such statistical process can be done only using an error function table.”
“I thought he said it was in ‘accep’ table,” Rajni mumbled. Luckily, it didn’t reach his ardent admirer’s ears.
“Now, let’s say there are m men standing in a circle. We need to find out who will be left after eliminating m-1 of them cyclically in steps of c. If we number them starting from 0 to m-1…”
“Shouldn’t we start counting from 1,” I put in. “In this case it is better to start with 0, as you will see,” he replied mysteriously. “Without loss of generality, we can assume that you start hitting person 0. We just have to figure out what the position of the last person will be.”
“Brilliant!” said my husband. “Wonderful. That solves the whole problem. I’ll just call them from zero to m-1 and start hitting zero.”
“But who will you hit finally?”
“The villain, naturally.”
“But what is the villain’s number? What we have to do is find out whom we end with if we start from zero. Then if we give the villain that number, he will be the last one. Do you see?”
He didn’t but shut up anyway.
“Let the villain have a number x.”
“‘x’ is not a number,” piped Rajni. Neither of us deigned to reply.
“When we are going forwards, at any stage, we skip c-1 people and hit the cth person. So we add c to the last person we hit, basically. If this exceeds the number of people at that stage, we just take the remainder, since they are standing in a circle. The remainder operation is called modulo, and can be represented by the ‘%’ symbol. So a%b is the remainder of a when divided by b.”
Saying this, he pulled out a sheet and started scribbling notes. I had the sense to take them back with me, and I have produced it here for completeness.
Let the number of the last person when there are people hit be f(m).
Then if there are only m-1 people, f(m-1) is the last person to be hit. If an mth person is added as number m-1, then we have m people now. But the position of the last but one person would have been effectively shifted back by m.
So f'(m-1) = f(m-1) – m
From that point onwards if we count c people, we end up with the last person as
f(m) = f(m-1) – m + c.
Since we must take the remainder for cyclicity,
f(m) = (f(m-1) – m + c) % m
f(m) = (f(m-1) + c) % m,
since m%m is 0. We know that f(1) = 0, since there is only 1 person. Hence by induction, the last person is known.
He went about explaining it, too, but neither of us could quite follow it. I therefore took it upon myself to ask “How exactly do we find out who the last is going to be?” What he said after that made sense.
“Suppose we don’t know how many people there are and we want to hit every fourth person. If there’s only one person, just start with 0, the first person. If there are 2, add four for the second person. But since the number 4 is invalid for just 2 people, take the remainder, which is 0. For three, again add 4 for the third person. 4 is larger than 3, and gives remainder 1. For 4 people, add 4 to 1, giving 5, which is larger than 4, giving remainder 1. This process can go on for as long as you want. For 5-10 people and a count of 4, the process is shown here.”
He was in fact kind enough to prepare a rather large table for upto 200 people and counting upto every 10th person, so my husband didn’t have to lose 1.5 crores by starting with the wrong person. The least he deserved under those circumstances, was in my opinion….
“Thank you very much, Anand. For your great help, I feel the least I can do is to give you my autograph.”
I thought it was the least too. But the boy seemed to think the world of it, and pulled out a rose autograph book. I couldn’t resist a quick look at the note.
“Yesterday I was a bus conductor. Today I am an actor. Tomorrow, who knows, I may even become a mathematician.”
— Lata Rajnikanth
Written in August 1994