Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2012-10-10 22:39:01

bluemist
Member
Registered: 2012-10-10
Posts: 1

### The Garden Problem

HI EVERYONE! Can you please help me with these. I already got some of it and answers are already in the net but what i really want is a step-by-step solution. I just made some guesses in some of them. I hope you could help out thanks

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. Pear is 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 growers don'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. Tulip is only in two gardens.
17. Apple is in a single garden.
18. Only in one garden next to 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?

Offline

## #2 2012-12-04 19:31:25

pRo9aMeR
Member
Registered: 2012-07-28
Posts: 44

### Re: The Garden Problem

I've done all of the other Einstein puzzles on the website but this one still eludes me as well, bluemist.

I posted an Einstein puzzle that I made a few months back.  To my knowledge, only one person here has solved it.  It's called "Who has the purple door?"

Offline

## #3 2012-12-04 21:21:02

bob bundy
Registered: 2010-06-20
Posts: 8,507

### Re: The Garden Problem

hi bluemist,

Welcome to the forum.

I'm sure there has been a thread on this puzzle but I cannot find it.  I'm reasonably confident I can take you through the steps.  Would you like it if we do the puzzle together using my method.  I think it will work.

You can start either with a big sheet of paper or (my preference these days) set out the information in a spreadsheet such as Excel.

Post back if you'd like to give it a try.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

Offline

## #4 2012-12-05 00:30:53

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,621

### Re: The Garden Problem

Hi all,

I solved this puzzle on the 23rd of July this year, but a check of all my posts near that date drew a blank.

I also tried searching using keywords such as "parsley", "onion", "Zick" and "Zick's", but nothing turned up except this thread.

My solution strategy was by process of elimination, using a grid that I drew up in Excel (see image of my starting grid).

As well as the main grid at the bottom, I also created a work area specifically for questions 4, 5 & 6.

Then, by reading, re-reading and re-re-reading the clues, and making eliminations along the way (just by deleting the letter in the applicable cell), I eventually came to the solution. Use of cell-fill colours helped visually.

Last edited by phrontister (2015-03-05 00:58:51)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

## #5 2012-12-05 06:07:59

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: The Garden Problem

Hi phro

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

## #6 2012-12-05 06:45:56

bob bundy
Registered: 2010-06-20
Posts: 8,507

### Re: The Garden Problem

hi phro,

Thanks.  Once you gave me the date I found my own Excel solution.

But bluemist wanted to know how to do it so I am trying to forget I know the answer, so I can go through how to get it from scratch.

Fortunately, my poor memory is an advantage when it comes to this approach.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

Offline

## #7 2012-12-05 11:19:20

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,621

### Re: The Garden Problem

Hi Stefy,

Yes, I use Excel quite a bit and enjoy it. It has a wide range of application, is very good at doing what it's designed for, and a lot of it is quite user-friendly too...which suits me. Compared to the wealth of knowledge out there in the wider Excel community, though, I'm just poking at it with a stick.

Hi Bob,

If we haven't posted about this puzzle before, I wonder how we came to do it at about the same time? ESP? Twins?

I'll watch this thread with interest (whoever that is) so I can learn from your step-by-step solution with bluemist.

Last edited by phrontister (2012-12-05 11:22:24)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

## #8 2015-03-03 01:56:21

patdools
Member
Registered: 2015-03-03
Posts: 1

### Re: The Garden Problem

Good morning - I've experimented with different ways to set this problem up, but have been pretty stumped. Bluemist - did you ever find the step-by-step solution you asked for? Phrontister - I really liked your Excel grid approach as well. If there are any more hints out there - I'd love to see them!

Offline

## #9 2015-03-03 04:28:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,621

### Re: The Garden Problem

Hi patdools,

While I solved this puzzle using the 'process of elimination' ("PoE") method I referred to in post #4, I think that Bob may have converted me over to using the 'insightful narrative' ("IN") method I described here.

'PoE' is generally the quicker of the two, but, as Bob said, it takes away some of the thinking. Solving it by the 'IN' method will most likely give you greater satisfaction, and I'd recommend going that way.

In fact, I just finished drawing up an 'IN' worksheet (in Excel) and am looking forward to giving that method a go.

Bed time first, though...

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

## #10 2015-03-04 03:38:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,621

### Re: The Garden Problem

Hi patdools,

Well, I solved it with 'IN'. :)

However, the reasoning turned out to be much the same as for 'PoE' because of the puzzle's unusual trick of having multiple varieties per crop. 'IN' seemed to me to be rather difficult to express in concise terms at times, so unless you want to grapple with that issue I'd recommend you use 'PoE'.

I've redone post #4's worksheet and have made it suitable for either strategy. The special work area for clues 4, 5 & 6 that I included in that earlier worksheet isn't necessary, so I've omitted it. Also, not all clues are needed to solve the puzzle: the solution route I take for both strategies doesn't need clues 5, 9 & 10, which I've marked as being superfluous.

The hidebox contains the new worksheet image, and you can choose which strategy to use:
(a) 'IN': ignore the four rows under the row beginning with "Position". Here is a link to an 'IN' info post.
(b) 'PoE': scan the clues (maybe multiple times!) and eliminate false entries from the grid containing the bold capitalised letters. Here is a link to a 'PoE' info post.
(c) Both strategies: enter solutions into the blank grid and your reasoning into the ruled section below the yellow highlighted row.

I enter the reasoning in numbered list form to aid with reviewing and referencing the content...which can also help to troubleshoot a blunder. The yellow highlighted line contains suggested notations for keeping entries concise.

You may prefer to set up your own spreadsheet for the benefits it gives, but a printout (preferably coloured) can be used away from the computer.

Enjoy! :)

Last edited by phrontister (2017-02-25 22:06:14)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline