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Gardens - Back to the Einstein's Riddles

Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).

1. They grow 12 different varieties.

2. Everybody grows exactly 4 different varieties

3. Each variety is at least in one garden.

4. Only one variety is in 4 gardens.

5. Only in one garden are all 3 kinds of crops.

6. Only in one garden are all 4 varieties of one kind of crops.

7. Pears are only in the two border gardens.

8. Paul's garden is in the middle with no lily.

9. Aster grower doesn't grow vegetables.

10. Rose grower doesn't grow parsley.

11. Nuts grower has also gourd and parsley.

12. In the first garden are apples and cherries.

13. Only in two gardens are cherries.

14. Sam has onions and cherries.

15. Luke grows exactly two kinds of fruit.

16. Tulips are only in two gardens.

17. Apples are in a single garden.

18. Only in one garden next to the Zick's is parsley.

19. Sam's garden is not on the border.

20. Hank grows neither vegetables nor asters.

21. Paul has exactly three kinds of vegetable.

Who has which garden and what is grown where?

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Gardens - solution

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  • 7 months later...

My Solutions process:

  • Write out clues and cross reference
    Ex: Nuts => gourd & parsley => no rose, no aster (Clues 9,10,11)
  • Write out limit: # variety & where or who
    Example = 2 cherries: #1, Sam; 1 apple: #1; 2 tulips: ?,?; ...


Luke in Garden #5
Who lives where?
Write who has what (so far)?
Who grows only 1 kind of crop?
Which variety is in 4 gardens?
Who has all 3 kinds of crops?
Re-check limits

Done!

Joshua S. Weinstein

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  • 4 months later...
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  • 1 year later...

I am new to this site, so I hope that I am not being too bold. Especially since I'm replying to a year+ old post. However, In onetruth's alternate answer, hint # 4 is not accounted for, therefore it is not possible.

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  • 3 weeks later...
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  • 2 months later...

It does work just be careful...

9. Aster grower doesn't grow vegetables.

10. Rose grower doesn't grow parsley.

11. Nuts grower has also gourd and parsley.

... These clues don't necessarily mean there is only 1 aster grower, 1 rose grower and 1 nut grower

1 - Hank - Apples, Pears, Cherries, Roses

2 - Sam - Cherries, Onions, Roses, Tulips

3 - Paul - Carrots, Gourd, Onions, Roses

4 - Zick - Aster, Roses, Tulips, Lilies

5 - Luke - Pears, Nuts, Parsley, Gourd

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  • 3 weeks later...

I have to say that clue 10 is badly phrased. I would submit that we want our students to correctly infer singulars and plurals from clues 9 and 11. I suggest that clue number 10 should read, "In no garden are both rose and parsley." As to the above statement that the clues 9-11 do not imply a singular garden appearance, I would ask for the proof that there is still a unique solution!

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  • 3 weeks later...

this is awsome-

Hank- Pear,Apple, Cherry,Rose Sam- Cherry, Onion, Rose, Tulip Paul- Carrot, Onion, Gourd, Rose Zick- Rose, Astor, Lilly, Tulip Luke- Pear, Nuts, Gourd, Parsely

Queequeg, i understand what you mean about the phrasing but since it is a riddle it should be stated in that sort of manner.

Jubjub, i'm not so sure grid would work, and if it does u would need a multi-dimensional grid which would cause an even bigger headache

Edited by vee's brain
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  • 2 months later...

I think clue 18 is badly phrased. It can be understood as:

Only in one of the gardens adjacent to zick's there is parsley.

But I could not find a unique solution to the puzzle when I inferred the clue this way.

So I think the meaning was supposed to be:

There is only one garden with parsley and it is next to zick's.

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