It’s been quite a while isn’t it? In my last post, I said that I’d be gone for a week but it turned out to be almost four months. During the last few months, I had to deal with some personal problems. I’m just glad that it’s all over now. So, I apologize for not informing you about my unexpected long absence, though during those times, blogging and the Internet as a whole were the last things on my mind.
But the most important thing now is that I’m back and I’m now excited to blog once again.
I found a curious puzzle in Sam Loyd’s Cyclopedia of 5000 Puzzles, Tricks and Conundrums, with Answers (1914). While several of the riddles and short puzzles from the book are either dated or mediocre, many of the puzzles in it are still great even by today’s standards.
The following puzzle is one of the few puzzles in the book in which Loyd didn’t provide a straightforward solution.
A dealer sold a bicycle for $50, and then bought it back for $40, thereby clearly making $10, as he had the same bicycle back and $10 besides. Now having bought it for $40, he resold it for $45, and made $5 more, or $15 in all.
“But,” says a bookkeeper, “the man starts off with a wheel worth $50, and at the end of the second sale has just $55! How then could he make more than $5? You see the selling of the wheel at $50 is a mere exchange, which shows neither profit nor loss, but when he buys at $50 and sells at $45, he makes $5, and that is all there is to it.”
“I claim,” says an accountant, “that when he sells at $50 and buys back at $40, he has clearly and positively made $10, because he has the same wheel and $10, but when he now sells at $45 he makes that mere exchange referred to, which shows neither profit nor loss, and does not affect his first profit, and has made exactly $10.”
It is a simple transaction, which any scholar in the primary class should be able to figure out mentally, and yet we are confronted by three different answers! Which in your opinion is right?
While this question may spark some interesting debates and arguments, the truth is this question can’t be answered without a vital information – the price the dealer paid for the bicycle when he first bought it. In other words, you won’t be able to calculate the profit without first knowing the real monetary value of the bike in the first place.
If you want to be philosophical about it though, you may either define the value of the bicycle based on the first, second or third transaction. If you choose the first transaction ($50), then the “profit” would be $5. For the second transaction ($40), the “profit” would be $15. Lastly, if you choose the third transaction ($45), the “profit” would be $10.
Of course, those are just all assumptions since there is no way for us to figure out how much it cost the dealer when he first obtained the bike. For all we know, the bike may have been given to the dealer as a gift!