Ambiguous Profit


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!

About Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. I blog at You can find me on Twitter @EdmarkMLaw and Facebook. My email is
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22 Responses to Ambiguous Profit

  1. Welcome back! I’ve heard this riddle before – it made my head hurt then too! 😄😉👍

    Liked by 1 person

  2. Garfield Hug says:

    Welcome back!! Glad all is well at your end! Now you have got my brain all boggled😝

    Liked by 1 person

  3. Benjay says:

    Just end the blog since no one noticed you were off? Take back your personal time. Blogging is stupid.


    • I think that ending my blog just because “no one noticed me” is more stupid. That’s only my opinion of course.

      Liked by 1 person

      • Benjay says:

        It is your reaction more than formed opinion. It was funny. Thanks. Mine is the popular response of the unblogging slightly cynical masses? You could offer an opinion on my reaction? My reaction is infotainment? Your blog is well done. If not, I would not read it. Thanks. Great response.

        Liked by 1 person

  4. Good to see you again, 8mark! This puzzle makes me feel two-tired! 「(゚<゚)゙??

    Liked by 1 person

  5. Sandi says:

    My husband is a math guy (aerospace engineering degree) and loves problems. I hate these things. But, it’s funny, this can be applied to the basic of basics. We see this happening when we have those online yard sales. Here’s a group of books just $10.00. All the kids books originally cost $6.00 (they show you the back cover with price) So you’re getting a “steal.” But some of those books were given to them or purchased at the dollar store. Sometimes they are trying to make a profit. Not the purpose of those Facebook group sites. They clearly state no buying something on sale, and trying to sell at higher amount. That is not what those sites are about…yet, you know people are doing it.

    Liked by 1 person

  6. comfykittea says:

    Welcome back! 🙂

    Liked by 1 person

  7. Andrea Frazer says:

    Totally going to read that to my son

    Liked by 1 person

  8. Nice to have you back!

    Liked by 1 person

  9. Thank you so much for following me, I’m honored! I’m impressed by your writings and I’m looking forward to read more of your work.
    Best regards,

    Liked by 1 person

  10. Welcome back! Sorry you had to deal with some personal issues but I’m glad all is well now 🙂

    Liked by 1 person

  11. Thanks for following my photo-blog ❤ I really appreciate it! For someone who is about as math-brained as a fence post (that would be me), I gotta admit this was good although I gotta admit my head was tilted a little after reading it and my brain isn't sitting in the same place either…


  12. cindy212 says:

    I read paragraph 1 over and over until I realized I was merely halfway through a cup of coffee. Heck, I considered getting a ledger out. Then I thought, what’s the initial balance (what the bike cost). But phttp. I am not a math gal)?


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