MIND GAMES
Unexpected result
Aditya Rishi

ALL the nation’s scientists, led by mathematicians, are put in one line, one after another, so that the first one sees everyone ahead of him (second through last), while the second sees the third through the last one, and the last one does not see anyone. A cap cap, either saffron or green, is put on each one’s head, so that the first one knows the cap colours of rest of them, but not his own, the second knows the cap colours of the third through the last one etc. The new minister asks each scientist, starting with the first one, what colour his cap is, and if his or her guess (which all others hear) is wrong, he or she is shot. The scientists are granted one last wish. They may agree in advance on what to do. Their only aim is to somehow minimise the casualties. That was in India six weeks ago. The future of mathematics looked bleak. However, there are still those who say that doomsday is far.

Here’s what Dr Vikas Handa has to say: "The future of mathematics is bright in India in spite of such politicians. It will be decided that the colour of the cap worn by next scientist will be announced by every odd numbered scientist and will be repeated by the even numbered scientist. Thus all even numbered scientists will be saved and half of the other half odd numbered one’s reply would be correct, by the law of probablitity. This will save nearly 75 per cent of the scientists."

Dr Tarsem Lal from Khanna has this in mind: "The only plan they can agree upon beforehand to minimise casualties is that the first man, nay mathematician, tells the colour of the cap of the last man in a voice loud enough to be heard by the last man. Last man keeps it in mind. The second man tells the colour of the second last man when colour of his hat is asked. The third man tells the colour of the cap of the third man from last and so on. In this way, they can ensure the safety of last half of the men. And in the first half, owing to probability, 25 per cent more will be saved. This scheme hopefully saves 75 per cent of the cream.

Rahul Khanna, a third-year mechanical engineering student at NIT, Jalandhar, makes them wish that they be told the number of each particular type of cap they have to wear, so that first, one can calculate how many persons are there, so total number of caps he can know and already knows how many of these are green how many are saffron. He can now count the number of caps on each head and know the colour less one to be able to tell the colour of the cap on his own head. As the next one hears his sound, by the same method he or she can also tell the colour of his or her own cap and keep the casualties to minimum.

"The scientists must tell the same colour, either saffron or green, respectively. This way, they can minimise their casualties. Because they do not know how many green caps and saffron caps are there," says Rajendra Prasad Yadawa, Gurukul Singpura, Jind Road, Rohtak.

Yes, they can agree that each odd-numbered scholar will say the cap color of the next one, so that the even-numbered scholars will survive, but can they do better?

They can save all but one, and the one they cannot save, the first one, cannot be saved with any tricks, since he has no information at all. It’s like this: the first scholar counts the saffron caps he sees and says saffron if this number is odd, and green if it is even. He meets his fate, but the rest of the scholars are saved: each one of them counts the saffron caps ahead of him, adds to the number of times the previous scholars (including the first one) said saffron, and, if the number is odd, he says saffron himself, otherwise he says green.

My highest regard is reserved for those who cannot separate saffron from green. The rest are just exit pollsters like me. It’s funny how election strategies can fail.

(Write at Mind Games, The Tribune, or aditya@tribunemail.com)