logic problems

Logic ProblemsLogic ProblemsLogic ProblemsLogic Problems

Lesson 1Lesson 1

Learning Objectives:• To use one piece of information to

see what effect it has.• To use a recording system to

organise the given information.• To check that the answer meets

the given criteria.

Meet my four volunteers:

Dawn Mark Josh Tina

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?

• CluesJosh 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.

So, how do we start?

• First we need to think about what we can learn from the information we are given.

• Each child could be called by each nickname, so let’s start there.

We’ll start by writing all four nicknames underneath each child.

Dawn Mark Josh Tina

Spider

We’ll can cross out each name as we decide it can’t be the correct one.

Dawn Mark Josh Tina

Spider

We’ve been given a number of clues to help us work out which nickname belongs to each child.

Here they are.

CluesJosh 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.

We now need to work carefully through the clues.

• With this type of problem it often makes sense to start with the first piece of information and work through them in order.

• However, that doesn’t always work.

• Don’t be surprised if you sometimes can’t learn anything from the first clue the first time you look!

The first clue tells us that Joshplays 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.

Let’s show that on our picture.

Dawn Mark Josh Tina

Spider

We could now go straight on to the second clue, but I think something

else makes more sense.Can you spot it?

We could now go straight on to the second clue, but I think something

else makes more sense.Can you spot it?

• That’s right! There’s another clue about Josh.

• Lets look at that one next.

The fourth clue tells us that Spider sometimes goes to tea

with Josh.What can we learn from that?

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!

If we add that to our picture, this is what we have.

Dawn Mark Josh Tina

Spider

What do we now know must be true?

Dawn Mark Josh Tina

Spider

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.

Dawn Mark Josh Tina

Spider

Clue number 2 tells us that Tinahas been on holiday with Curly

but travels to school with Fudgy.

Clue number 2 tells us that Tinahas been on holiday with Curly

but travels to school with Fudgy.

• So we know that Tina’s nickname cannot be Curly or Fudgy.

Dawn Mark Josh Tina

Spider

Does that help us learn anything for certain?

No, so we move on to another clue.

There’s just one more clue we haven’t looked at.

• The third clue tells us that Spider, Curly and Dawn play in the football team.

There’s just one more clue we haven’t looked at.

• 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.

Dawn Mark Josh Tina

Spider

We already knew Dawn couldn’t be Fudgy so she must be Ace. And… ?

Dawn Mark Josh Tina

Spider

No one else can be Ace.

Dawn Mark Josh Tina

Spider

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?

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?

What can you see?

Dawn Mark Josh Tina

Spider

Tina must be Spider!

Dawn Mark Josh Tina

Spider

Dawn Mark Josh Tina

Spider

Mark cannot be Spider, so he must be Curly.

Dawn Mark Josh Tina

Spider

Our solution to the problem is:

• Dawn ~ Ace

• Mark ~ Curly

• Josh ~ Fudgy

• Tina ~ Spider

• 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?

• 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!

Like with the car-parking problem, the pictures are great, but we’ve

had to write the nicknames out four times. There must be a more

efficient way. Any ideas?

Like with the car-parking problem, the pictures are great, but we’ve

had to write the nicknames out four times. There must be a more

efficient way. Any ideas?

This type of problem works very well set out as a table.

Write each name down one side and each nickname along the top.

Spider Curly Ace Fudgy

As we work through the clues again, we can add ticks or

crosses in the boxes, depending on what we have learnt.

Josh cannot be Curly or Ace.

Josh x xTina

Josh cannot be Spider sohe must be Fudgy.

Josh x x x √Tina

No one else can be Fudgy.

Dawn xMark xJosh x x x √Tina x

Tina cannot be Curly or Fudgy.

Dawn xMark xJosh x x x √Tina x x

Dawn cannot be Spider or Curly.

Dawn x x xMark xJosh x x x √Tina x x

Dawn must be Ace,so no one else can be.

Dawn x x √ xMark x xJosh x x x √Tina x x x

Tina must be Spider,so no one else can be.

Dawn x x √ xMark x x xJosh x x x √Tina √ x x x

Mark must be Curly.

Dawn x x √ xMark x √ x xJosh x x x √Tina √ x x x

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 iseasy to draw and read

Dawn x x √ xMark x √ x xJosh x x x √Tina √ x x x

Now it’s your turn!!

SandwichesSarah, Jenny, Ranjit and Paul each choose a

sandwich filling. They can choose from:~ tuna,~ 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?

logic problems

joshplays tennis

given information

themso joshs nickname

piece of information

given criteria

dawn play

football team

number of clues

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