Thursday, September 5, 2013

The Past Asks You: Apple Economics, 1698

Johann Hermann Knoop, Pomologia (1758)
It's time for another puzzle from the past:
"A man sent his three Sons to Market, to his Eldest he gave twenty two Apples: To the second sixteen: and to the third ten Apples, and bid them sell all at a price, and bring all Money alike." 
T. T. A Rich Treasure (1698)
To review: each son has to sell all his apples. No son can set a higher price than his brothers. And each of them has to bring home the same amount of money as the others. How will the clever trio accommodate the economically incoherent demands of their father?

If you think you have what it takes to be a 17th-century apprentice fruit vendor, post your answer in the comments. I'll add the 1698 solution tomorrow.


  1. Since they are to sell "all" at a price, they can either sell all the apples in a batch for a single price and divide the money between them; or they can agree to sell their share of the apples for the same fixed amount: the oldest can sell his 22 apples for the same price that the middle sells his 16 and the younger sells his 10.

  2. The obvious solution is to give all the apples away. Same price for all, and each brother returns with the same amount. Not very wise economically...

  3. Eldest son eats 12 apples, second son eats 6 and all 3 sell 10. And then I think they will need to ask the past how to cure stomach aches.

  4. Chydenius before SmithSeptember 5, 2013 at 2:52 PM

    Am I a boring one if I suggest that the youngest apple-seller first buys six apples from his oldest brother and another six from the middle-boy, who also first buys six apples from his big, bad brother (for the market price!) and then the younger ones will re-sell them to the fool customers who want to have more apples they can eat, hence everyone selling 22 times an apple?

    I know, I ruined all the fun.

    Let's say that there came a highway robber who took all the apples. So, everyone sold all their apples for 0 gold pieces. It's all fair, isn't it?

  5. Hmm. If not for your modern paraphrase, I'd be inclined to think it's a catch question exploiting the ambiguity of the phrase "sell all at a price." It's perfectly easy, after all, for each son to sell all of his apples "at a price" and bring home the same amount of money -- they don't have to set the same price if you read the sentence that way. It's also perfectly possible for them to sell the apples "all at a price" and bring home the same amount of money, as long as the first and second sons don't sell all of their apples. What they can't do as easily is sell all of the apples "all at a price," but since there's only one "all" in the original puzzle, their father hasn't demanded that they do that.

    But the paraphrase seems to knock that out, so I vote for setting the price at zero.

  6. Excellent solutions!

    Here's the official answer: "They sold them thus, a Servant coming to buy Apples for his Lady, bought all their Apples at seven a penny, leaving the odd ones behind, then the eldest Brother had 3 d. and one Apple left, the second Brother 2 d. and two Apples left, and the youngest brother 1 d. and three Apples left: They being liked by the Lady, he came to buy the rest, and then the price was raised, and they would have a penny an apple for what was left, which being given, the Eldest sold his one for 1 d. the second sold his two for 2 d. and the third his for 3 d. so every one carried 4 d. home."

    What the Lady thought about this price-fixing is not known.

    1. Wow, I guess that Lady really like apples.

    2. If the Lady's servant is willing to pay a penny per apple right after he bought them at seven per penny, he must have a side deal selling them to some other servant who is even worse at math.

    3. You know, if the Eldest had just given the youngest six apples, they'd all have had sixteen apples to sell....