Dream star

I HAVE always dreamt of meeting men of scientific temper like Jayant Narlikar, a star among astronomers in India. I learnt that this star would enter the orbit of our city to deliver a lecture in the Physics Department of Panjab University.

I got up and ready earlier than usual on the day of the lecture because this was an appointment I could not afford to miss. The professor was delightful as ever in his speech and even invited me over to his place afterwards.

I reached the guest house earlier than usual when the professor was occupied in his work, surrounded by telescopes, stop watches and charts. He said this was his way of having a night out. He examined me for a while and said, "So, you like stars." "Yeah, particularly Jackie Chan," I said, at which, wrinkles appeared on his forehead like the third eye of Shiva. To control the situation, I quickly said, "These stop watches on your table are fabulous." "Yes, but can you tell me which is the odd one out of these?" he said.

There were five stop watches on the table, as shown in the figure here, of same make, design and size. I deduced that the difference had to be elsewhere and pondered over the solution of the problem for a while. The watches had only the hours’ hands that pointed at 1, 4, 6, 8 and 9, respectively. For a while, I thought that these numbers were in series, but it was not so. There were two odd numbers and three even ones, so, none could be singled out. "Time up!" said the professor, "You failed to notice that only the first watch pointed at a number that was prime. A prime number is divisible only by 1 and itself."

Realising my disappointment, he decided to give me another chance and asked me if I would like to solve one more problem. After I accepted the challenge, he said, "I have five star charts — a hexagon with one star, a rectangle with three stars, a pentagon with five stars, a circle with seven stars and a triangle with four stars — and you have to pick the odd one out of these." The circle, as shown in the second figure here, looked odd to me, but the professor said it was not the one. After much thought, I said, "It looks to be an out of the world problem." "You presume correctly. These charts show position of stars that are out of this world, unlike Jackie Chan," said the professor. "Observe that the number of stars and angles (or sides) in all figures, except the pentagon, add up to seven," he said. "Look at the figures now, what do you see?" "Stars," I said. "Stars! What stars? Wake up silly," I heard my father say, "it is 11.30 now, don’t you have to attend Narlikar’s lecture?" I realised that it had indeed been a dream encounter with my star.

— Aditya Rishi