"PROFESSOR Stephen Hawking has agreed to have you as his caretaker on my recommendation. I have told him that you have talent, but it is for you to prove it now. If you do it, he will make you his assistant and teach you more about mathematics, which is what you want," says a senior professor to a young research scholar. "I have heard that time is his obsession," says the student. "It is true and that is why you should be careful. Good luck," says the senior professor.

"Time to readjust the clocks," says Dr Stephen Hawking, Lucasian Professor of Mathematics at Cambridge and author of A Brief History of Time, to his caretaker. "Professor, why do you always readjust all the clocks in your house at 9 pm everyday?" says the caretaker. "There is nothing unusual about it. Most persons in the world readjust their clocks according to the start time of prime-time programmes on television," says Stephen Hawking. "I would like to do this for you today," says the scholar.

"I do not move the hands on a clock to readjust it, just the numbers," says Hawking. The shocked scholar finds his speech just in time to say, "How is that possible, Sir?" "It is for you to find out. Leave six adjacent numbers on the face of this clock intact and rearrange the other six in such a way that the sum of every pair of adjacent numbers is prime," says the man who knows all about time.

"It is easy professor. Keep adjacent numbers 11, 12, 1, 2, 3 and 4 intact and move 7 in place of 5, 10 in place of 6, 9 in place of 7, 5 in place of 9 and 6 in place of 10. You can also keep the same adjacent numbers intact and replace 5 with 9, 6 with 10, 8 with 6, 9 with 5 and 10 with 8. In both cases, the sum of every pair of adjacent numbers is prime," says the scholar.

Leave as many numbers as possible on the face of this clock intact and rearrange the rest, so that the sum of every pair of adjacent numbers is composite (not prime)

Hawking says, "That was quick thinking. Now, leave as many numbers as possible on the face of this clock intact and rearrange the rest so that the sum of every pair of adjacent numbers is prime." The student says, "I need only four moves or two swaps (position interchange) for that." He interchanges 11 with 1 and 8 with 4. The sum of every pair of adjacent numbers is now prime. After this, he interchanges 10 with 2 and 8 with 4, with the same result. "How did you find the correct sequence?" says the Professor.

"Sir, a clock has three pairs of numbers on its face — (4 and 5) (7 and 8) and (10 and 11) — that make a composite sum, so, at least a number from each of these has to be moved to arrive at the combination that we want. This means that at least four moves are required to rotate either an even number or an odd number from each of these pairs," says the student.

Hawking says, "The prime reason why I accepted you to be my caretaker was to see how talented you were. It is my decision to remove you instantly from your current position... and accept you as my assistant. Join me at the prime time tomorrow."

— Aditya Rishi