Problem Solving Strategy Use Matrix Logic

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 we’ll 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.

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 isn’t 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.

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.

As we work through the clues again, we can add circles or crosses in the boxes, depending on what we have learnt.

Write each name down one side and each nickname along the top. Spider Curly Ace Fudgy Dawn Mark Josh Tina

The first clue tells us that Josh plays tennis with Curly and 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 Josh’s nickname cannot be Curly and it cannot be Ace.

Josh cannot be Curly or Ace. Spider Curly Ace Fudgy Dawn Mark Josh x Tina

Clue number 2 tells us that Tina has been on holiday with Curly but travels to school with Fudgy. So we know that Tina’s nickname cannot be Curly or Fudgy.

Tina cannot be Curly or Fudgy. Spider Curly Ace Fudgy Dawn Mark Josh x Tina

Does that help us learn anything for certain Does that help us learn anything for certain? No, so we move on to another clue.

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.

Dawn cannot be Spider or Curly. Ace Fudgy Dawn x Mark Josh Tina

Spider cannot be Josh’s nickname either! The fourth clue tells us that Spider sometimes goes to tea with Josh. What can we learn from that? Spider cannot be Josh’s nickname either!

Josh’s nickname must be Fudgy!! What else do we therefore know? If Josh’s nickname is Fudgy, no one else can have that nickname. Let’s add that to the diagram.

x O No one else can be Fudgy. Spider Curly Ace Fudgy Dawn Mark Josh Tina

Dawn must be Ace, so no one else can be. Spider Curly Ace Fudgy Dawn x O Mark Josh Tina

Tina must be Spider, so no one else can be. Curly Ace Fudgy Dawn x O Mark Josh Tina

Mark must be Curly. Spider Curly Ace Fudgy Dawn x O Mark Josh Tina

We’ve looked at all the clues once. At this point it’s always a good idea to look though the clues again to check you haven’t missed anything. Have we? No, so all the information we need must now be on our picture. Can we learn anything else?

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.

A clear solution that is easy to draw and read Spider Curly Ace Fudgy Dawn x O Mark Josh Tina

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!

Now it’s your turn!!

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 doesn’t like fish. Jenny cannot eat dairy products. Ranjit does not eat meat or fish. Jenny doesn’t like tuna or chicken. Which sandwich filling does each child choose?

Sandwiches Tuna Egg Salad Cheese Chicken Sarah Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny O Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X Jenny O Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X O Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X O Jenny Ranjit Paul

Sandwiches Tuna Egg Salad Cheese Chicken Sarah X O Jenny Ranjit Paul

Solution Sarah – Chicken Jenny – Egg salad Ranjit – Cheese Paul - Tuna

Who’s Who at the barbecue? Tom, John, Fred, and Bill each brought his favorite meat to barbecue. From the clues below, determine each man’s occupation and favorite meat. Tom is neither the nurse nor the teacher. Fred and the pilot play in a jazz band together. The burger lover and the teacher are not musically inclined. Tom brought hot dogs. Bill sat next to the burger fan and across from the steak lover. The secretary does not play an instrument or sing.

Make a chart (matrix).

Mark traits (ignoring musical cues).

Combine with musical clues (perhaps using adjunct list).

Eliminate possibilities.

Act on eliminated possibilities and eliminate more.

Substitute Fred’s food marks at bottom of nurse column.

Act on eliminated possibilities and eliminate more.

Cross-correlate “Secretary” and “John.”

Eliminate possibilities and act on eliminated possibilities.

Read off solution. Tom – Pilot - Hdog John – Scty - Burg Fred – Nurse - Steak Bill – Tchr - Chkn

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.