The Case of the Milliner’s Carpet
“Come in and sit down, my dear”, ushered Holmes to the young lady, as Mrs Hudson withdrew to attend her other duties, “it’s a long walk from Tufnell Park, and if you want to talk to me about a financial matter then I expect you’ll need to compose yourself.”
“Why yes, Mr Holmes,” she stammered, “However did you…?”
“From your collar, madam.” The young lady’s expression betrayed her incomprehension. Holmes continued. “The detail on your collar is of a thread which is not generally available. That shade of blue is particular to Mrs Crowthorne’s millinery in Holloway; you will not see its like elsewhere in England until you travel as far north as Lincoln. Evidently you work for Mrs Crowthorne — your hands confirm your occupation — and you have, shall we say, borrowed some of the thread from the shop to decorate your jacket.” She lowered her eyes at the transparency of her misdemeanour, “The state of your boots suggest you have a one mile walk to your workplace each day. Given the weather today and the dampness of your coat it is clear you just caught the last of the rain as you left your house. That means you live fifty to sixty minutes away, given your height and constitution, which places you either in Tufnell Park or Liverpool Street, and given the way you pronounce your Rs I think we can rule out anything east of Holborn, don’t you?”
“And the…?”
“Financial matter?” suggested Holmes, who was clearly enjoying a little sport, “the flakes of paper on your dress are from the kind of notebooks only used by a bookkeeper — they are available in very few stationers. It’s clearly a matter you have been worrying about recently. Now, pray tell us, what exactly is keeping you awake at night?”
“My name is Annabelle Silperton, Mr Holmes,” she began, “I’m a… well, of course you know that. My husband, Nicholas, and I have not been married long, and our rooms are on the second floor of a terraced house. We save hard to keep things nice, and you must believe me, Mr Holmes, when I say we cannot afford everything we would like.”
“Mrs Crowthorne is not known for her generosity,” observed my friend.
“I couldn’t possibly…” Young Mrs Silperton trailled off, then managed to recover herself. “Just recently,” she continued, “I broached the subject with my husband of a new carpet for the stairway in our building. The present one is terribly old and worn, and although visitors do not comment on it I know they are disappointed with what they have to walk on. I had found just the thing, and after a slightly rough-looking youth had visited to take measurements I received a quotation for £12, including fitting.”
“That would be from Oberon Retinue, I presume?” Holmes paused to indulge in the young lady’s obvious surprise before going on. “The cost of carpets is tied precisely to floor measurements, which invariably are odd values, leading to pricing to the degree of pennies. Oberon Retinue is the only carpeteer east of Shepherds Bush who habitually rounds his prices for convenience. His convenience.”
“No doubt you are right, Mr Holmes. However, the matter of vexation is not the price of the carpets. What troubles me, sir, is the forthcoming conversation with our neighbours, Mr and Mrs Asquint, on the first floor. You see the carpet is to run only on the stairs to the first floor, and then continue to our rooms on the second. The couple on the ground floor will not get use of the carpet. It will only be used by the Asquints to walk to their rooms on the first floor, and by us to access our rooms on the second.”
Mrs Silperton paused as if to muster suffient energy to control the obviously gathering turmoil within her.
“Mr Holmes,” she pleaded, “I don’t know how we should split the cost with Mr and Mrs Asquint.”
A silence descended on the room and after a moment I could bear it no longer.
“Why, it’s obvious!” I exclaimed, “Fifty-fifty. You pay £6 and your neighbours pay £6.”
Mrs Silperton looked aghast, while Holmes gently lowered his head into his left palm to hide his embarrassment.
“Oh no, Dr Watson,” gasped the milliner, “Oh no, that wouldn’t be right at all. The Asquints would use the carpet less than us, so they should pay less than us. They would use the stretch only to the first floor, while we would use the stretch to the first floor and then the next stretch to the second floor.”
Mrs Silperton turned her attention back to my companion, clearly a more understanding listener, while I shrunk back in my chair, vowing not to be so foolish again.
“Mr Holmes, my husband and I disagree about how the cost should be split. My husband reasons that we would use the carpet twice as much as the Asquints: they would use it to one floor, and we would use it to one floor and then to the next. Thus our share should be twice their share. We should pay £8 and and they should pay £4.”
Mrs Silperton paused so that we could take in this logic.
“Yes, that’s quite clear,” I offered, “£8 and £4. Now that you explain it like that it’s obvious.”
“No, Dr Watson, it’s not obvious at all,” she sighed, looking at me with evident unhappiness. From the corner of my eye I could see Holmes peer over at me, pityingly. Mrs Silperton continued.
“My reasoning, sir, is this. The carpet is in two equal stretches: from the ground floor to the first, and from the first floor to the second. Mr and Mrs Asquint would only use that first stretch — the first half. However, they should only pay what they use of that first half. And that first half would in fact be used equally both by them and by us. Thus they make half the use of half the carpet — one quarter. Similarly we use three quarters of the carpet. So we should pay £9 and they should pay £3.”
The young lady was now frantic with worry, and looked pleadingly over to the world-famous detective.
“Mr Holmes, please help me. How should we divide the cost of the carpet?”
“Well, Holmes, this is a conundrum indeed,” I ventured, “Would you say this is a three pipe problem?”
Holmes raised his eyebrows as he turned to me slowly.
“No, Watson, I would not. The matter is elementary. The solution is clear.”
Can you match Sherlock Holmes’s amazing powers of reasoning? How should the cost of the lady’s carpet be divided?
