One fine spring day, Mr. and Mrs. Filbert and their two sons (Bart and
Jack) planted four young trees on their property.  From the following
clues, find out where each tree went and who planted it:
-It was agreed that in addition to the maple and the tree planted by
Mrs. FIlbert there should be a tree to shade the side of the house and
another to shade the patio.
-The poplar was not planted in front.
-Bart dig a deeper hole than did Mr. Filbert or the person working at
the side of the house.
-Mr. FIlbert gave advice to Jack once or twice, but none to the person
at the back fence or the one planting the oak.
-Mrs. Filbert thought the ash and the tree planted in front were both
prettier than the one she planted.

Based on the logic of my own mind, I deducted that Mr. Filbert planted
the Maple Tree in the front, Jack planeted the poplar tree on one side
of the house, Mrs. Filbert planted the oak tree on the other side of
the house, and Bart planted the Ash Tree in the back.  This was merely
a game of "process of elimination" with the clues.  Instead of
figuring out who planted what where, you have to look at who didn't
plant what where.

The only one I'm not 100% sure about, is which tree is on which side. 
I'm positive about the front and the back, though.


Hope this helps!

Toobis

Here's the answer:

Mr Filbert planted the maple in the front.
Mrs Filbert planted the poplar in the back.
Bart planted the oak by the patio.
Jack planted the ash on the side.

Here's how you get it.

From reading the problem, we know that:
Mrs. F did not plant the maple.
The maple is not on the side or the patio.
Mrs. F did not plant on the side or patio.
The poplar is not in front.
Bart did not plant on the side.
Mr. F did not plant on the side.
Mr. F did not plant in the back.
Mr. F did not plant the oak.
The oak is not in back.
Jack did not plant the oak.
The ash is not in front.
Mrs. F did not plant the ash.
Mrs. F did not plant in front.

From all this we can determine:
Jack panted on the side because the other 3 did not.
This means that Jack did not plant the oak because it can't be on the side.

Mrs. F planted in the back because she is already ruled out from the
other 3 locations.
This means the maple has to be in the front, because we already know
it is not on the side or patio,
and it can't be in the back because Mrs. F did not plant the maple.

We have already determined the oak is not in the back or side, so with
the maple in front the oak must be on the patio.
We know that Mr. F did not plant the oak, so he wasn't on the patio,
and Jack was on the side,
and Mrs. F was in back, so Mr. F planted the maple in the front.

The only spot left for Bart is the patio, which means he planted the oak.

We know Mrs. F did not plant the ash, so Jack must have.

That leaves Mrs. F with the poplar.

You don't think I'm going to pass this up, either, do you, lol.
Here's my graphical approach for getting there. We're all saying the
same thing, just different ways of getting there.

First, I translated all the "clues" into "NOT-" arguments (numbers
refer to lines of clines, numbered as 1-5)
 
MR F, 3. Not side, 4. Not Back Fence, Not Oak
MRS F, 1. Not Maple, Not side, Not patio 5. Not Ash, Not Front
Bart, 3. Not Side of House
Jack, 4. Not Back Fence, Not Oak   
 
Maple, 1. Not Mrs. F, Not Side, Not Patio
Poplar, 2. Not Front
Oak, 4. Not Back Fence, Not Mr. F, Not Jack
Ash, 5. Not Mrs. F, Not Front
 
Side, 1. Not Mrs. F, Not Maple 3. Not Mr. F., Not Bart
Patio, 1. Not Mrs. F, Not Maple
Front, 2. Not Poplar, 5 Not Ash, Not Mrt. F
Back Fence, 4. Not Jack, Not Mr. F, Not Oak
 
Second, I Set up Grids, Names on Y Axis, Column for Trees (4
subcolumns), Column For Location (4 subcolumns)
Maple/Poplar/Oak/Ash   Side/Patio/Front/Back Fence
 
Each entry in the grid is a "no" for that column (except X = marks the spot)
1-5 = Number of Argument that EXCLUDES that Person
A-F= Number of Conclusion, in order, that leads to next step after 1-5 is marked.
X = Remaining Answer
 
Here's the full solution:
 
X,C,4,D   3,D,X,4     MR F
1,X,B4,5   1,1,5,X    MRS F    
E,C,X,F   3,X,E,B    BART
A1,C,4,X   X,A,A,4    JACK
 
Here's how you get there: (It's easier if you draw up a grid and
follow along)...you'll see where the "therefore, not" entries come
from as they come up).
 
First 2 (A, B) Solutions: Jack = Side (only Jack choice left
vertically in locations), Mrs. F = Fence (only Mrs. F choice left
horizontally in type of trees)
 
A. Therefore, Jack = Side
    A.1. If Jack = Side, Jack Not Maple
 
B. Therefore, MRS F = Back Fence
    B.1. If Mrs. F = Fence, Then Maple = Front
    B.4. Then Mrs. F Not Oak
 
C. If A, B, Then Mrs. F = Poplar
 
D. If C, Then Mr. F = Maple
    Therefore, Mr. F = Front (See B.1)
 
E. Therefore, Bart = Poplar 
    Therefore, all "locations" are solved
 
F. If C, Then Jack = Ash
    Therefore, Bart Not Ash
    Therefore, Bart = Oak
    Therefore, all "trees" are solved
 
Mr F, Maple, Front
Mrs. F, Poplar, Fence
Bart, Oak, Patio
Jack, Ash, Side
 
I'm sure there are more elegant ways to derive this...I used the "back
of envelope" method with methodology dimly recalled from a class
25-years ago, lol. Given the subsequent translation from the envelope
into typing, there were many "gremlin" opportunities, so feel free to
question any line. And don't hold me to the "technical" meaning of the
"logical operators" I used. But this gets you to the answer....if that
was the goal. If the intervening equations are necessary, you should
probably point that out and I'll defer to an official answerer with
fewer missing neurons.

After reading again, I guess I only agree with jchaumont. Sorry toobis! lol

The paragraph I wrote as First 2 (A, B) Solutions: Jack = Side (only
Jack choice left vertically in locations), Mrs. F = Fence (only Mrs. F
choice left
horizontally in type of trees)

Should instead be:

First 2 (A, B) Solutions: Jack = Side (only Jack choice left
vertically in locations), Mrs. F = Fence (only Mrs. F choice left
horizontally in LOCATIONS). (All the Trees are "solved" values.

Yes, I also used a piece of paper and a lot of not statements.  I only
wrote the whole thing out in sentences because I didn't think people
would get my scribblings.  :)  I didn't apply quite the formal rigor
that you did though - I am glad you did because it would be useful for
me to learn that method and apply it elsewhere.

I came to the same conclusion as both jchaumont & ssmithfl but my
method was a lot simpler. I call it the Cluedo method after the famous
board game (Colonel Mustard in the library with the candlestick etc.)

Simply get hold of twelve squares of paper and write down each of the
four members of the family, the four types of tree planted and the
four locations.

Under the name of each person, arrange a piece of paper with the tree
and a corresponding location. Can be in any order to begin with.

Then rearrange the squares of paper as you follow the various clues.
Your answer will appear very rapidly!