MIND GAMES
Test of character
Aditya Rishi

The short moustached man, whom the green men called boss, showed me a slip, which he said was the passport to our freedom. On it was written the product of two integers >=2, and simultaneously the sum of the same two integers was given to Sachin. Hence, I only knew the product and Sachin only knew the sum of the two integers. However, both were aware that the first knew the product and the second knew the sum.

I was then asked whether I could determine the two numbers, and I answered no, loud enough for my partner to hear. Sachin was then asked whether he could determine the two numbers, and he too answered no, loud and clear. I was then asked once again whether I could determine the two numbers and this time the answer was... yes!

Do you remember the times? Well, it lay forgotten till my memory jogged back to me. Who got us out of trouble that day, I still can’t recall, but it was some test of character. Don’t ever think that the Tests are over. "It ain’t over till it’s over." Baseball great Yogi Berra said that, even though he didn’t really say what all he said.

Your toughest examination is the one ahead. College, school, university are like playing in the under-19 league. Mental toughness is what will get you there and using your brain will lead you to mental toughness. We all know the road that leads to using our brain. Of course, some don’t have to take that road. They take the aerial route.

There’s an explanation about that day: 2*2=4 and 2+2=4, given by Gursimran Singh. Well it’s a guess. In international cricket, we don’t guess. We watch the ball, and you can observe a lot just by watching. I didn’t say that; Yogi did. Does that explain?

"From the solution, you have the product 12 and Sachin has the sum 8. Since integers are >=2, you have two possibilities: 3,4 and 6,2, so you say no, expecting Sachin to have two possibilities of sum 7 and 8. If Sachin has 7 as sum, he will expect 3,4 or 2,5. Clearly both numbers can’t be prime, as you will then readily guess the numbers. Hence, Sachin will expect 3,4, but as he says no, 3,4 can’t be a possibility, so the sum can only be 8. Now 8=2+6 and 4+4 will make Sachin say no since he knows 3*4=2*6=12 and 2*8=4*4=16 will make you say no. Hence, you conclude the sum to be 8 and the numbers 2 and 6 on hearing Sachin’s no, which makes you say yes."

Amarinder Gill and Ankit Garg of Thapar Institute of Engineering and Technology, Patiala, have come up with this. That’s more like Test cricket. Park slogging is not their game. There’s another purist: Tarsem Mohan. He plays in exactly the same way, which is the correct way of playing at such a delivery.

When you get an extra delivery, capitalise on it. It’s a gift afterall; take it. The smallest number with two permissible product decompositions is 12=2*6=3*4. PS (parting shot): When you call, it should be loud enough for your partner to hear. I think that’s what saved us that day. Write at Mind Games, Windows, The Tribune, or aditya@tribunemail.com.