Saturday,  January 20, 2001
M I N D  G A M E S

The great train snobbery

GABBAR SINGH and his gang plan to loot the Haripur Express. This will be the most daring of all train robberies, if they succeed. A night before they are to strike, somewhere in the ravines near Ramgarh, Gabbar is discussing the plan for the last time with his men. All his men, except Sambha, are mathematicians. However, Sambha is a snob who is always sure of himself and thinks that he is the greatest mathematician of them all.

"Sambha," Gabbar shouts. "Huh... yes Sardar, did you call me?" Sambha says after jerking out of his dream. "Fool! What were you doing while we were making the strategy ó trying to solve Fermatís last theorem?" says Gabbar. "Sardar, you are a genius, how did you guess that?" It takes Kalia and Jagira to hold Gabbar down.


Gabbar says, "Look Sambha, you are my second-in-command and the success of this plan depends on you. If you act like this, how are we going to rob the train?" "Trust me Sardar, just tell me the plan once again," says Sambha. "Hereís the plan," says Gabbar, "we move from here at 12, when the clock has both hourís and minuteís hands pointing in the same direction. We strike when the hands point in the same direction again." "That is easy," says Sambha. Gabbar says, "Is that so! Tell me how many minutes will it be until the next time the hands point in the same direction?"

"After exactly 12 hours, when the clock strikes 12 again. See, I told you it was easy," says Sambha. "Pig! You will get all of us killed," Gabbar yells. "Why do you say so Sardar?" says Sambha. Gabbar, who is trying hard to regain his composure, says, "The minuteís hand moves around 1/60 of the dial in one minute, and the hourís hand moves 1/720 around. If t is the number of minutes, then t/60=1+t/720. Solving the equation gives us t=65 and 5/11 minutes. The hands come together at equal intervals eleven times between noon and midnight, so there is 12/11 hours between them."

"Ah! I see more clearly now, Sardar, I had the same solution on my mind. I was only joking," says Sambha. "I donít like bad jokes," the bandit king hisses. He says, "Hereís the revised plan. Sambha will wait in the cabin above the rail track. I have placed two candles inside the cabin that have the same length, but one will burn down in seven hours, while the other in eleven. I will light the two at the same time and, except Sambha, all of us will move out and hide behind the rocks. The train will pass by the cabin when one candle will be twice as long as the other. When it happens, Sambha will give us a signal to come out and rob the train?"

Sambha is waiting inside the cabin with a gun and a red handkerchief in his hands. Suddenly, the wind blows out the two candles and moments later, the train passes by, but Sambha does not get to know it. After waiting for several hours, he comes out of the cabin and approaches Gabbar.

"Why didnít you give us the signal?" says Gabbar. "The candles blew out," says Sambha. Gabbar: "Did you note the time when I lighted the candle?" Sambha: "Yes Sardar." Gabbar: "Budhead! You should have calculated the time when one candle would have become twice as long as the other." Sambha: "Impossible, tell me how would you do it."

Gabbar, who is angry and crying at the same time, says, "The big candle burns t/11 of its height in t hours, so the fraction remaining after that time is (1-t/11). For the narrower candle, the fraction remaining is (1-t/7). The narrower candle will be shorter, so the equation is (1-t/11)=2(1-t/7). Solving this equation gives us t=77/15 hours, or 308 minutes. It was so easy, peabrain, and you blew it. Now, prepare to die."

Gabbar arranges the digits 1 to 8 as follows: 8, 5, 4, 1, 7, 6, 3, 2. "The digit 9 is not there. This is not justice. Where should the digit 9 be put in this order, I donít know? However, if Sambha puts it where it belongs, he will be spared." The digits are produced before Sambha, while a jackal calls in the background.

Sambha, the snob who cannot rob, finds that the digits are in an alphabetic order. Therefore, he puts the digit 9 between the 4 and the 1, where it belongs. Sambha smiles and then breaks out into a laugh and Gabbar and his men follow suit.

ó Aditya Rishi