My son was doing some math exercise and encountered this question:

„Na, wie war’s?“, ruft meine Mutter aus dem Garten, als ich vom Pilzesammeln komme. Ich breite die Pilze auf dem Tisch aus und rufe zurück: „Mehr als die Hälfte sind Maronen. Drei davon sind leider madig, und diese drei sind mehr als ein Viertel der Maronen.“

„Dann weiß ich, wie viele Pilze du höchstens gesammelt hast“, ruft meine Mutter. Es sind
(A) 21 (B) 14 (C) 19 (D) 24 (E) 16

As I understand, a child was collecting mushrooms and counting them. Amongst all of them, more than half are chestnuts, 3 of them are bad, the 3 are more than 1/4 of the chestnuts. So there are maximal 11 chestnuts because 12/4 equal 3. What confused me is why counting mushrooms and chestnuts together, the answer is 21. I let my son ask his teacher, she says it's 21 but did not tell why.

Is there something special in the language part, that makes the math different?

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  • @HubertSchölnast: As a native speaker, I would be utterly confused by the implication that someone would (accidentally?) pick up chestnuts while searching for mushrooms. I have never heard of that mushroom type and I don't think it is commonly known (at least by that name?) here in South-Western Germany. Good find! – O. R. Mapper Dec 31 '16 at 16:32
  • @O.R.Mapper Maronen are common in the Black Forest. I know them by that name only. But must admit that my teacher wasn't a dialect speaker. – Stephie Dec 31 '16 at 16:39
  • @Stephie: Interesting. To me, Maronen have always been Esskastanien and nothing else, and no vendor of Maronen that I have come across (on Christmas markets etc.) felt a need to specify they were not offering mushrooms. – O. R. Mapper Dec 31 '16 at 16:47
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    @O.R.Mapper as usual: context is key. – Stephie Dec 31 '16 at 16:52

Well, the child in the question was picking and counting mushrooms, in this case a special type of edible mushrooms with the full name Maronen-Röhrling, colloquilally often shortened to Marone amongst mushroom pickers and cooks.

The edible chestnut Marone plays no role in the quiz.

Note that both the mushroom and the tree seed are named for their colour: chestnut-brown.

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    So when they say 'Maronen', they are simply a short work for one kind of mushroom, like 'Kuli' for 'Kugelschreiber'. For me this is more like a language question than a math question. Thanks and happy new year! – Tiger Hwang Dec 31 '16 at 13:04
  • @TigerHwang exactly. For the math problem, replacing "Pilze" and "Maronen" with another generic / special term pair like "Fish" and "Trout" or "Fruit" and "Apples" would be equally valid. – Stephie Dec 31 '16 at 13:21

No there is nothing special, I think you missed only one important word: "höchstens". Which means maximum here. So the mother does not give the correct number of mushrooms but the maximum number of all the collected mushrooms. So there is still a range of possible solutions left but never more than 21. Only this can derived from the statements given.

Side note: "Marone" in Germany can be both "chestnut" and "bay bolete". In the case of a mushroom it is always "bay bolete". In Austria, Switzerland and Southern Germany the edible chestnut is also known as "Maroni".

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    I don't think the math is a problem once one realizes that "Marone" is the mushroom, not the chestnut. See my answer below. – Stephie Dec 31 '16 at 10:47
  • I don't think so, the OP simply mixed "chestnut" and "bay bolete" but there are still other mushrooms in the quiz not named. – Thomas Dec 31 '16 at 10:57

There are two conditions here:

More than half of the mushrooms X, are chestnut mushrooms, Y.

Three of the chestnut mushrooms, Y, are bad, and those three account for at least one-fourth. Three is more than one fourth of Y, so Y is >= 11.

Plugging back 11 into the previous equation, More than half of the mushrooms X, are chestnut mushrooms, 11, means that X is <= 21. Two other answers, 19 and 14 also work, but the teacher wanted the maximum number, "höchstens".

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