The M1M1 treasure hunt, week 8
"Oh Dr Watson," Mrs Hudson called out as I shut the door of 221B against the chilly autumn wind. "He's bought a Christmas tree. Dragged it all over my carpets, he did. Made a frightful mess."
Thus warned, I ascended the stairs. In the centre of the room, rather than the Scottish pine I was expecting, there stood something more of the Citrus variety, bearing several spheroidal yellow fruit.
"What is that Holmes?" I asked bewilderedly.
"A lemon tree, my dear Watson."
"Honestly, Holmes. You carted that thing up here, for the sake of a bad pun?"
"No Watson, I believe it will help me defeat that arch-villain Moriarty. He is a deadly foe, a mathematical genius. I told you he once wrote A Treatise On The Binomial Theorem?"
"You did, Holmes. And I must admit, I can't picture a mathematician being as evil as you portray, or even mean."
"Therein lies his dreadful cunning! In his treatise he explains how the binomial series for non-integer powers is an Infinite version of the Mean Value Theorem. In other words, he considers it a theoretical proof of the Value of Infinite Meanness!"
"But why the lemon tree?"
"I have been blind, Watson. In Moriarty's paper, at one point he states that `only by the careful study of these lemons can the enquiring student hope to comprehend the final result.' Naturally I assumed at the time, that "lemons" was a misprint for "lemmas". For like many pure mathematical works, it was an almost unreadable morass of lemmas, propositions and corollaries. But at last I have realised that he was mischievously affording us a clue, that these yellow fruit hold the key to countering his Machiavellian schemes."
"But how? I suppose we could start by working out their volume. Let's see - each one is an ellipse rotated around its long diameter. About 6cm long and 4cm wide, so that makes
"Excellent Watson, you surpass yourself," muttered my companion. But how can we discern his dastardly intent? I need more data!"
"Surely a Professor must have written other papers?" I enquired.
"Watson, I am again in your debt. He wrote `The Dynamics of an Asteroid.' I have a copy somewhere. In contrast to his first work, this, being an applied paper, is full of unstated assumptions, questionable logic and misleading illustrations. Furthermore, it is obsessed with the equations which happen to govern the real world, rather than the more interesting general case."
"Look, Holmes!" I cried, pointing at a diagram, which depicted an asteroid of prolate shape and a curiously yellow hue. "Another lemon!"
"The plot thickens, Watson. The text considers the complicated motion of a body spinning about a precessing axis."
So saying my friend immersed himself in the highly technical details. He emerged after a while and asked,
"Watson, If I integrate a function f(t) between t=x2 and t=x4, what is the x-derivative of the answer evaluated at x=1?"
"That tallies. Bizarrely, Moriarty has calculated the general motion of a spinning lemon, with particular reference to the position of the funny end-bit. Now why would anyone throw lemons around?"
"Quite so, Holmes. As the American ambassador remarked yesterday, `If life gives you lemons, make lemonade.' He's actually officiating at a lemonade-making contest today, if my memory serves."
In a flash, my companion grasped the significance of this. "That must be it, Watson! Moriarty plans to assassinate the ambassador of our former colony. Doubtless he has manufactured some grenade-like device with the pointy nodule on the end acting as a firing pin. We must make haste to save him!"
"Are you sure, Holmes? There have been several implausible plots these last few weeks, but this seems the most unlikely of all."
"Watson, as I have frequently observed, when you, er, lemonade
the impossible, whatever remains, however improbable, must be the truth."
I grabbed my old service revolver. We sped across London, dashed into the lemonade exhibition, just in time to hear the
ambassador announce:
"Before I award the prizes, I've been asked to demonstrate the American art of lemon squeezing. Could someone please toss me a lemon?"
"Here, Your Excellency," called out a tall, shadowy figure 1m in front of us at (0,0). He lobbed a lethal lemon along the parabolic path
ky=(8x-x2) to hit the ambassador who stood 8m further away from us in a straight line, at the same height.
Here, k was a constant I didn't have time to work out, for my companion cried
"Hand me your pistol, Watson!"
To avoid hitting the crowd, Holmes carefully fired the gun as high as possible, hitting the lemon tangentially to its path.
He thus disabled the dastardly device, which detonated at a decent distance.
Moriarty span round and stared fixedly at my companion. "We shall meet again, Holmes," he vowed coldly and strode out.
"That was close, sir," the ambassador thanked us. "It was diagonally 6.5m from me, when you hit it, and even nearer to you."
This enabled me belatedly to determine the value of the constant k.
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Week 8
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