Saturday, July 3, 2004
 MIND GAMES Return of Batman Aditya Rishi Do you remember the time? "What time?" Do you remember the rhyme? "Oh, that I remember: It's close at the start, but Jack is running three times as fast, and by the time they are off this escalator, Jack has stepped on 75 stairs, while Jill has stepped on 50, and is far from the gladiator. They wonder in amazement, they wonder in the lab, how many stairs does the escalator have? How is it, how is it, they ask the translator, how's its speed related to the speed of the competitors? Were they running with or against the escalator?" Yes, that's the one I am talking about. Now I shall reveal my most treasured possession: the medal. The length is 100 stairs, Jack and Jill were running along the escalator which was moving with the same speed as the slow Jill. In the time the fast Jack stepped on 75 stairs, the slow Jill could step on only 25, so, since she stepped on 50, she spent twice as much time on the escalator as the fast Jack. Therefore her speed relative to the ground was half that of the fast Jack, and therefore the escalator's speed was the same as the speed of the slow Jill, and she counted exactly half the stairs. There are many other ways to go about it. Do you know how I got the answer? I read this batsign in the night sky over this city: "Dear Aditya, I am back, but I don't think you will recognise me. Anyway, it's getting dark and I must get to work. First, the reply to the Bull Run: First let us assume the total number of steps to be 'T'. Let the speed of Jill be 'U' (consequently, Jack's speed will be 3U) and the speed of the escalator be 'V' { speed measured in steps per second: V +ve if the direction of movement of the escalator is with Jill and vice versa} . The net speed of Jill will be U+V, and the net distance { in terms of steps} will be 'T'. Time taken will be { T/U+V} . The same situation can be observed w.r.t. the escalator. Here, the speed of Jill will be 'U' and the distance { steps} travelled will be 50. Time taken will be 50/U. Since the time is the same, we have the equation: { T/U+V=50/U} . Similarly, for Jack, we have this equation: { T/3U+V=75/3U} . Solving the two equations, we get U=V. This means that the speed of the escalator is the same as that of Jill and in the same direction. Putting U=V in any of the equations, we get T=1OO. This means that the total number of steps in the escalator was 100. Seems like this case has been solved. Your's Batman { 9993-note this} " Dr Vikas Handa from Giessen (I know it's somewhere on the map, but where?), Ravneet Kotwal from Jalandhar and Shubeg Gill from nowhere sent in answers that were far, far better and shorter, but the one that came from the batcave had that element of mystery in it. I am he, the Riddler, and this puzzle is destroying my mind: who is the man behind the bat, or is it a woman behind the cat? Meeeeeow, I smell a rat. Rhyme time isn't over yet; the Riddler will return, Batman, and then there will be no hiding from me. Hu, ha, ha, ha, ha. (Write at Mind Games, Saturday Extra, The Tribune, or aditya@tribunemail.com