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"Oh my God, I can’t see a thing. Is that the hurricane?" "Yeah, but not the business end of it. You have only 25 minutes to cross the bridge outside your town. Leave now." After one or two minutes of it, I get a message from doctor’s cellphone. "I am stuck here at the bridge. I need your help." "What is it doc?" "We are a family of four trying to cross this bridge at night. One needs a flashlight to cross the bridge, and only two persons can cross it at the same time, moving at the speed of the slower of the two. I can cross the bridge in one minute, my wife in two minutes, my child in five minutes and my mother in 10. What is the fastest way for us to cross the bridge?" "Doc, this is no time for riddles." "I’m serious." "Okay, give me six weeks then." "Six weeks? @#$%!*&@%$!..." That was six weeks ago. He hasn’t called me since then, but I know he’s fine. Let us meet the daring rescue squad, starting from the slowest. "The family will require 24 minutes to cross the bridge. First, the doctor crosses with his wife and takes 2 minutes to do so. Then his wife returns and then crosses the bridge again with the child, taking a total time = 2+5 = 7 minutes. Then, the child returns to his grandmother and finally both cross the bridge, taking a total time of 5+10 = 15 minutes. So total time taken = 2+7+15 = 24 minutes." This is how Brahm Kiran Singh analyses the situation. Sorry Brahm, but the doctor didn’t have that much time, because he had already wasted 4-5 minutes in talking to me over cellphone after I had told him about the 25-minute limit. "It will take the family 19 minutes to cross the bridge. Doctor and his wife cross first and wife being slower of the two, they both cross the bridge in 2 minutes. Then the Doctor will get back to get the rest of the family and he will take 1 minute to cross the bridge. Next, he crosses with his son and they take 5 minutes to cross the bridge and then the doctor again goes back and takes 1 minute. Lastly, he crosses the bridge with his mother and they take 10 minutes to cross, so the total time the family takes to cross the bridge is 2 + 1 + 5 + 1 + 10 = 19 minutes." This solution is from Arshdeep Singh of New Vijay Nagar in Jalandhar City. Dr Vikas Handa (Giessen) and Ravneet Verma hold the same opinion. "Your doctor friend and his family can be saved in 17 minutes. The fastest probable way is: 1) Wife and Man cross + Man returns = 3 minutes. 2) Son and Mother cross + Wife returns = 12 minutes. 3) Man and Wife cross + no one returns = 2 minutes. Total time = 17 minutes." This is from Anurag Saxena, a class XII non-medical student (Bhavan Vidyalaya, Chandigarh) who lives in Pinjore; Varun Jindal (also of class XII), who lives in Patiala; and Viney Yadav, who I believe is from IIT, Chennai. Their trick is to send the slowest people together. I can only agree with you, guys. There’s time for one more solution, from Vimal Jit Kaur. "The family crosses the bridge in 11 minutes and 36 seconds. Since doctor’s mother can cross the bridge in 10 minutes, I have imagined 10 points on the bridge and also assumed that flashlight can show light from starting point till the end of the bridge. "First, the mother with any one of the three, say the doctor, starts to cross the bridge. Mother holds the flashlight. When doctor in on the other end of the bridge, mother is at point 1. Now she turns to show the light to one of the two, say the child. Since the child can cross each point in 1/2 min (5/10 min), mother waited for 1/2 min for the child and total time she has taken till point 1 is 1+1/2 min. In the next 4 1/2 min, the child crosses the bridge and the mother is in the middle of 5th and 6th point and takes 1 1/2 + 4 1/2 = 6 minutes to reach this point. She turns to show the light to doctor’s wife. His wife takes 12 seconds (2/10 = 1/5 mins = 12 secs) to cross each point and she will take 1 mins and 6 secs to cross mother. This waiting time is again added to mother’s time, i.e. 6 + 1 mins 6 secs = 7 mins 6 secs. Mother has taken 4 1/2 more mins to cross the remaining 4 1/2 point’s distance. The total time taken by the family to cross the bridge is 7 min 6 secs + 4 1/2 min = 11 min 36 secs." Now that’s what I call twisting the Constitution. The doctor wasn’t in such a hurry after all; he made it in 17.
(Write at Mind Games, The Tribune, or aditya@tribunemail.com) |
