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Comment by thom | Hacker News Reader

With clojure.core.logic:

  user> (run* [q]
          (fresh [morning afternoon a b c d e f]
            (fd/in morning afternoon a b c d e f
                   (fd/interval 0 35))
            (fd/eq
              (< afternoon morning)
              (= (+ a b) 10)
              (= (+ c d) 16)
              (= (+ e f) 26)
              (= (+ (* morning a) (* afternoon b)) 35)
              (= (+ (* morning c) (* afternoon d)) 35)
              (= (+ (* morning e) (* afternoon f)) 35))
            (== q [morning afternoon a b c d e f])))

  Spoiler warning, scroll right:                                                         ([5 0 7 3 7 9 7 19] [7 0 5 5 5 11 5 21] [35 0 1 9 1 15 1 25])

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All of these solutions have the sale of chickens for $0, which makes the problem easy (eg, they each sold 7 chickens for $5 and gave the rest away), but is surely not in the spirit of the question.

Selling the chickens for $0 is not just "not in the spirit of the question", it's plain wrong! By definition, you can't "sell" something for $0, that's giving it away.

For example, one dictionary defines "sell" as "to exchange (something) for money". $0 is not money. It's literally nothing.

I don't know why people (not you) come up with "clever" solutions that violate the plain wording of the question.

I would have thought it obvious: it looks like a lateral thinking puzzle to some people, and it's painfully common to have the null case be a part of the solution (in a sort of perverted aha-gotcha! attempt).

After all, part of the linked article's point was how it struck him as potentially broken; if the problem seems broken, then many will heuristically start attacking the problem itself rather than the math. And once the problem's no longer trusted to be stated as exact and correct, well, a simple pedantic jump in meaning is a pretty small step. (I'll concede it's possible you've never come across a broken 'clever' math word problem before, but having found enough to be wary myself - both in school and college - I'm rarely surprised at people leaping for the lateral thinking solution.)

Clearly I was distracted by IBM selling its chip business yesterday for -$1.5bn.

Ha, yes. Reading the question, and indeed giving it any thought at all, were always the things that held me back in maths at school. Using cents and requiring > 0:

  user> (run* [q] (fresh [morning afternoon a b c d e f] (fd/in morning afternoon (fd/interval 0 3500)) (fd/in a b c d e f (fd/interval 0 26)) (fd/eq (< afternoon morning) (> morning 0) (> afternoon 0)
																		    (= (+ a b) 10) (= (+ c d) 16) (= (+ e f) 26) (= (+ (* morning a) (* afternoon b)) 3500) (= (+ (* morning c) (* afternoon d)) 3500) (= (+ (* morning e) (* afternoon f)) 3500)) (== q [morning afternoon a b c d e f])))

  Spoiler warning, scroll right:                                                    ([375 125 9 1 6 10 1 25])

The only odd thing about this answer is that farmer 1 apparently decided to lower prices after selling 9 of his 10 chickens in the morning...

n.b. Correct answer. Took me 20 minutes with paper and pen: 5 minutes of noodling and 15 of constructing a table and winnowing it quickly using an insight about relatively prime numbers.

And using computers instead of my head, that was another pitfall.

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