"WE'LL rescue anyone from anywhere. Just call us," the young corporal is watching the advertisement on the TV when he realises that he is late for the morning parade. He reports to the sergeant who is in no mood to show mercy. "Well soldier, we have a situation on ‘the bridge too far’. Do you think you can handle it?" says the sarge in a voice that could silence lions in a circus ring. "Yes Sir." the corporal’s voice echoes on the ground.

At the bridge, the sergeant gives the offender a frightening stare, the one that freezes the equatorial sun. "The General wants to know the height of the bridge by this afternoon. Find it and tell him or I’ll tell you." "Do I get any equipment to measure the height of the bridge Sir?" the corporal yells. "Sure, the Army equips its soldiers well. Here; take this ruler," says sarge and leaves.

The corporal, who can fight 50 enemies alone, is badly stuck now. Then, on his cell phone, he dials a number he had seen on TV in the morning, following which, a man comes there and says that he is the rescuer. "I told you the situation, yet you bring nothing to measure the height of the bridge," says the corporal. Rescuer: "Believe me, you don’t need anything except your mind in most situations. Some things in life are bad; they can really make you mad; don’t grumble, give a whistle; and always look on the bright side of life! If life seems jolly rotten, there’s something you’ve forgotten; that life’s a laugh and death’s a joke; it’s true, you’ll see it’s all a show; keep ’em laughing as you go; and always look on the bright side of life."

"My life is in chaos at the moment," says the corporal. Rescuer: "Remember what Ian Stewart said, that chaos is lawless behaviour governed entirely by law." Corporal: "Why are you so full of quotes," "Remember Abe Shenitzer, who said: one can use mathematics without knowing much of its history, but one cannot have a mature appreciation of mathematics without a substantial knowledge of its history."Corporal: "Mathematics?"

Rescuer: "Yes, your best rescuer. One good way to estimate the height oaobject. We’ll measure the height of this bridge in this way. What’s your height?" Corporal: "Six feet." "Good!," says the rescuer and makes the corporal stand next to the bridge tower. He holds the ruler so that the corporal appears to be one-inch tall. The height of the roadway on the bridge then appears to be four inches and that of the supporting tower ten inches. The rescuer estimates that the roadway is 24 feet above the ground and the tower is 60-foot high.

"That roadway is actually 26 feet above the ground; I know it," says the corporal. Rescuer: "I see! The error was because I did not hold the ruler in a precisely vertical position." Corporal: "Now, you’ll have to calculate it all over again."

Rescuer, "As Alfred North Whitehead said, the study of mathematics is apt to commence in disappointment; but I don’t think that we need to recalculate. According to a basic theorem of projective geometry, if we have four straight lines in a plane through a common point and a fifth one intersecting these, then the ratio of the ratios of some sections of the fifth line is independent of the position of the fifth line. In our problem, this yields a single equation: (1/4)/((10-1)/(10-4))=(6/26)/((x-6)/(x-26)). Solving for x, the height comes out to be 78 feet."

Corporal: "Thanks, what can I do for you?" "As Dr Seuss said: think! Think and wonder. Wonder and think. How much water can 55 elephants drink?" The corporal keeps thinking... and misses the afternoon deadline.

(Write to the writer with alternative solutions to the bridge problem at adityarishi@kasparovchess.com)