With a little bit of luck

PROF Higgins’ car breaks down on a lovely Sunday morning in London, which is a bit unfortunate if you consider that a distinguished and charming lady is waiting for him at that moment in Buckingham Palace, where the annual ball-room dance is about to begin.

At the Victoria railway station, a plainly dressed Elizabeth Doolittle is pacing up and down the platform, carrying a bucket full of flowers in one hand and a mirror in the other. She has not been able to sell a single flower today so far. Another misfortune, you might say. However, God sees, but waits. Prof Higgins does not have his car and Elizabeth does not have a platform ticket, so they board a train — to avoid walking and station officials, respectively.

"Mister, do you want some flowers. These are at 10 pence each and I will give you one free with every two you take," says Elizabeth to Higgins. Such lack of manners in a woman shocks Higgins, a typical London-high-society product. "Use the brain to sell your product. I am sure no one has bought your flowers today," says Higgins. "Luck does more for the poor than brains, mister. What do you do?" Liz says. "I am a professor of mathematics," says Higgins. "Is that all you do?" says Liz. "Dear lady, it is tough being a mathematician because you have to use your brain," says Higgins. "I know mathematics, too, but I consider it more a matter of luck," says Liz. "Why?" says Higgins.

Liz snatches a paper from Higgins and writes 321 on it. She holds it against the mirror and shows it to Higgins. "Look I have reversed the number without touching it," she says. The mirror image of the number is 123, obviously. "Amusing!" says Higgins and has a good laugh, "However, can you find the smallest number, the mirror image of which is its multiple. The number has to be greater than 1." "I give up," says Liz after much thought. "The number is 1089 (9801/1089=9). Besides the mirror-image number, the other multiple of each of such numbers is either 4 or 9 (9*1089=9801; 4*2178=8712) and no other number. You can insert as many 9s as possible in the middle of numbers like 1089 or 2178 and still have a reverse multiple. 9*10999999999989 = 98999999999901 and 4*21999978 = 87999912."

"I admit that logic can help you sometimes, but luck can make you happy more often," says Liz. "That is true indeed. It was luck that brought us together and you made me laugh, something that I had been missing for so long," says Higgins. "I, too, learnt the importance of logic from you, Sir" says Liz. "I will buy all your flowers for being so polite to me and I would also like to take you with me to the Queen’s ball right now," says Higgins. Liz says, "Oh Sir! You are most kind, but how will I pass off as a lady at the party?" "With a little bit of luck, my fair lady," says Higgins, with a smile.

— Aditya Rishi