M1M1 Treasure Hunt

The M1M1 treasure hunt, week 4


One chilly autumn afternoon, I sat ensconced with my boon companion in 221B Baker St, intent on the daily paper.
"You are troubled, Watson," observed the great detective. "Your brow is furrowed, your eyes are glazed and distant, while you constantly chew your lip, muttering inaudibly. Might I possibly be of some assistance?"
"It's nothing, Holmes. I'm trying my hand at a crossword puzzle. Take this clue for instance: `Digestive canal: 10 letters'."
"Alimentary, my dear Watson," he replied after a moment's deliberation.
"By Jove, Holmes, you're right. How do you do it."
"My work frequently requires the solution of puzzles. See what you make of this singular missive, which arrived this morning." So saying, he passed me a piece of notepaper.

"Dear Mr Holmes," I read out loud. "I am most horribly afraid. I work at a top university. Last week a collaborator of mine was killed along with his entire workforce in an industrial explosion, following a visit from a mysterious Mr Bond. A Bayesian risk analysis indicates with 95% confidence that it was no accident, but the police won't listen. I have come to you during my lunch hour, but you are out. I am at my wits end - if I am still alive tomorrow, I shall try again."

I pondered. "The writer appears in considerable distress, but he has left us nothing to go on. We don't know where he works."
"Come Watson, you know my methods. Apply them! The handwriting is clearly that of a youngish woman - witness the impression of her fingers on the paper. If you sniff the letter you will detect the unmistakeable odour of bicycle oil, mingled with the leaves of the Red Oak, a tree growing only in Hyde Park. I have written a monograph on the subject. She cycled North to Baker St during her lunch hour, she works at a top, not-too-distant, university. She is obviously an expert in Probability. There can be no doubt as to her identity nor workplace. And she is clearly in great danger."
"Then what are we waiting for, Holmes!" I leaped up.
"We are waiting, Watson, for the cab I ordered twenty minutes ago, which I now hear outside."

"How can we enter the building, Holmes? We have no ID card."
"Ah Watson - mathematicians rarely memorise formulae, provided they can work them out again. See here!" Scratched above the lock was the instruction:
"Raise e to the power e. Raise the result to the power e. Take the logarithm and raise the result to the power e. Take the logarithm and raise 2 to the power of the result. Square the result and take the logarithm. Divide by e and take e to the power of the result."



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"Utterly ridiculous, Holmes," I muttered as we sped through the confusingly identical corridors of the Huxley building, towards Dr McSpy's office. The door was locked but above the numerical keypad, was written:
Enter the coefficient of x4 in the MacLaurin series for (5x-1)/(3x2-4x+1).


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The door creaked open. The office was empty, but bore the unmistakable signs of interrupted statistical endeavour. Generating functions had been knocked to the floor, while maximum likelihood estimators were scattered untidily over the desk. "Too late, Watson!" cried Holmes, "But if the worst has happened, we'll avenge her."
A scrap of paper, in the large curly writing beloved of her students, offered the only clue. It read
"4cos4θ-2cos2θ+sin22θ+5,
where θ is the square of Prof Thomas' favourite real number."



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