Crossing the River with Dogs

1
Problem Solving Strategy
Use Matrix Logic
2
Use Matrix Logic

• A matrix is a two-dimensional chart that is used
  to organize information in a problem.
• A matrix can use the process of elimination in a
  systematic way.
• One way to improve your logical reasoning ability
  is to solve logic problems. The basic idea
  behind these problems is to solve them by
  matching items in various categories.
• Most logic problems can be solved by using a
  chart or a table that well call a matrix. Using
  a logic matrix sets up a one-to-one
  correspondence between elements in a problem.
• Graph paper can make it easier to create/draw a
  matrix to work with.

3
Use Matrix Logic

• Although you might tend to focus naturally on
  what must be true in a problem, it becomes even
  more important to pay attention to what isnt
  possible when working with this problem solving
  strategy..
• Matrix logic is a strategy based on things that
  cannot be.
• One of the really successful actions of good
  problem solving is to read, re-read, and read the
  clues/problems over and over again and it is the
  very backbone of this problem-solving strategy.
• Continually reviewing the clues gives your brain
  an opportunity to connect more and more
  information, eliminate more and more information,
  and reach a solution.
• Enjoy the challenge and expand the thinking
  ability of your brain.

4
Nicknames

• Dawn, Mark, Josh and Tina are friends.
• They each have a nickname.
• Their nicknames are Spider, Curly, Ace and Fudgy,
  but not in that order.
• What is the nickname of each of the friends?
• Clues
• Josh plays tennis with Curly and goes swimming
  with Ace.
• Tina has been on holiday with Curly but travels
  to school with Fudgy.
• Spider, Curly and Dawn play in the football team.
• Spider sometimes goes to tea with Josh.

5
As we work through the clues again, we can add
circles or crosses in the boxes, depending on
what we have learnt.
6
Write each name down one side and each nickname
along the top.
Spider Curly Ace Fudgy
Dawn
Mark
Josh
Tina
7
The first clue tells us that Joshplays tennis
with Curlyand goes swimming with Ace.

• What does this tell us about Josh?
• It tells us that Josh cannot be the same person
  as Curly or Ace, if he does activities with both
  of them
• So Joshs nickname cannot be Curly and it cannot
  be Ace.

8
Josh cannot be Curly or Ace.
Spider Curly Ace Fudgy
Dawn
Mark
Josh x x
Tina
9
Clue number 2 tells us that Tinahas been on
holiday with Curlybut travels to school with
Fudgy.

• So we know that Tinas nickname cannot be Curly
  or Fudgy.

10
Tina cannot be Curly or Fudgy.
Spider Curly Ace Fudgy
Dawn
Mark
Josh x x
Tina x x
11
Does that help us learn anything for
certain?No, so we move on to another clue.
12

• The third clue tells us that Spider, Curly and
  Dawn play in the football team.
• So that must mean that Dawn cannot be Spider or
  Curly.

13
Dawn cannot be Spider or Curly.
Spider Curly Ace Fudgy
Dawn x x
Mark
Josh x x
Tina x x
14
The fourth clue tells us that Spider sometimes
goes to tea with Josh.What can we learn from
that?

• Spider cannot be Joshs nickname either!

15
Joshs nickname must be Fudgy!!

• What else do we therefore know?
• If Joshs nickname is Fudgy, no one else can have
  that nickname.
• Lets add that to the diagram.

16
No one else can be Fudgy.
Spider Curly Ace Fudgy
Dawn x x x
Mark x
Josh x x x O
Tina x x
17
Dawn must be Ace,so no one else can be.
Spider Curly Ace Fudgy
Dawn x x O x
Mark x x
Josh x x x O
Tina x x x
18
Tina must be Spider,so no one else can be.
Spider Curly Ace Fudgy
Dawn x x O x
Mark x x x
Josh x x x O
Tina O x x x
19
Mark must be Curly.
Spider Curly Ace Fudgy
Dawn x x O x
Mark x O x x
Josh x x x O
Tina O x x x
20
Weve looked at all the clues once.

• At this point its always a good idea to look
  though the clues again to check you havent
  missed anything.
• Have we?

• No, so all the information we need must now be on
  our picture.
• Can we learn anything else?

21
With a table like this, you can see very easily
whether it works or not, as there can only be one
tick in each row and each column.Always
remember to re-read the original details to check
that your solution fits the criteria you were
given.
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A clear solution that iseasy to draw and read
Spider Curly Ace Fudgy
Dawn x x O x
Mark x O x x
Josh x x x O
Tina O x x x
23
Our solution to the problem is

• Dawn Ace
• Mark Curly
• Josh Fudgy
• Tina Spider

• Look back at the criteria and clues for the
  problem.
• Does this solution fit with the information we
  were given?
• Yes it does so we are correct!

24
Now its your turn!!
25
Sandwiches

• Sarah, Jenny, Ranjit and Paul each choose a
  sandwich filling. They can choose from
• tuna,
• egg salad,
• cheese, or
• chicken.
• Each child chooses a different filling.
• Clues
• Sarah doesnt like fish.
• Jenny cannot eat dairy products.
• Ranjit does not eat meat or fish.
• Jenny doesnt like tuna or chicken.
• Which sandwich filling does each child choose?

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Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah
Jenny
Ranjit
Paul
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Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X
Jenny
Ranjit
Paul
28
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X
Jenny X
Ranjit
Paul
29
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X
Jenny X
Ranjit X X
Paul
30
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X
Jenny X X X
Ranjit X X
Paul
31
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X X
Jenny X O X X
Ranjit X X X
Paul X
32
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X X X
Jenny X O X X
Ranjit X X O X
Paul X X
33
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X X X O
Jenny X O X X
Ranjit X X O X
Paul X X X
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Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X X X O
Jenny X O X X
Ranjit X X O X
Paul O X X X
35
Sandwiches
Tuna Egg Salad Cheese Chicken
Sarah X X X O
Jenny X O X X
Ranjit X X O X
Paul O X X X
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Solution

• Sarah Chicken
• Jenny Egg salad
• Ranjit Cheese
• Paul - Tuna

37
Whos Who at the barbecue?
Tom, John, Fred, and Bill each brought his
favorite meat to barbecue. From the clues below,
determine each mans occupation and favorite meat.

1. Tom is neither the nurse nor the teacher.
2. Fred and the pilot play in a jazz band together.
3. The burger lover and the teacher are not
   musically inclined.
4. Tom brought hot dogs.
5. Bill sat next to the burger fan and across from
   the steak lover.
6. The secretary does not play an instrument or sing.

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Make a chart (matrix).

39
Mark traits(ignoring musical cues).
40
Combine with musical clues (perhaps using adjunct
list).
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Eliminate possibilities.
42
Act on eliminated possibilities and eliminate
more.
43
Substitute Freds food marks at bottom of nurse
column.
44
Act on eliminated possibilities and eliminate
more.
45
Cross-correlate Secretary and John.
46
Eliminate possibilities and act on eliminated
possibilities.
47
Read off solution.
Tom Pilot - Hdog John Scty - Burg Fred
Nurse - Steak Bill Tchr - Chkn
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Strategy Use matrix logic

• Mark traits from clues.
• Combine clues.
• Eliminate possibilities and act on eliminated
  possibilities.
• Substitute.
• Cross-correlate.
• For other approaches or problems Study the
  introduction, and test assumptions.