Logic Problems Lesson 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? 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.

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 Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

We’ll can cross out each name as we decide it can’t be the correct one. Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

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

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 Josh plays tennis with Curly and goes swimming with Ace.

What does this tell us about Josh?

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.

Let’s show that on our picture. Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

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?

Spider cannot be Josh’s nickname either!

If we add that to our picture, this is what we have. Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

What do we now know must be true? Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

Josh’s nickname must be Fudgy!!

What else do we therefore know?

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.

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 Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

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.

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

Does that help us learn anything for certain?

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 Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

We already knew Dawn couldn’t be Fudgy so she must be Ace. And… ? Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

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

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 Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

Tina must be Spider! Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

And? Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

Mark cannot be Spider, so he must be Curly. Dawn Mark Josh Tina Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy Spider Curly Ace Fudgy

Our solution to the problem is: Dawn ~ Ace Mark ~ Curly Josh ~ Fudgy Tina ~ Spider

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?

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!

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. SpiderCurlyAceFudgy Dawn Mark Josh Tina

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. SpiderCurlyAceFudgy Dawn Mark Josh xx Tina

Josh cannot be Spider so he must be Fudgy. SpiderCurlyAceFudgy Dawn Mark Josh xxx√ Tina

No one else can be Fudgy. SpiderCurlyAceFudgy Dawn x Mark x Josh xxx√ Tina x

Tina cannot be Curly or Fudgy. SpiderCurlyAceFudgy Dawn x Mark x Josh xxx√ Tina xx

Dawn cannot be Spider or Curly. SpiderCurlyAceFudgy Dawn xxx Mark x Josh xxx√ Tina xx

Dawn must be Ace, so no one else can be. SpiderCurlyAceFudgy Dawn xx√x Mark xx Josh xxx√ Tina xxx

Tina must be Spider, so no one else can be. SpiderCurlyAceFudgy Dawn xx√x Mark xxx Josh xxx√ Tina √xxx

Mark must be Curly. SpiderCurlyAceFudgy Dawn xx√x Mark x√xx Josh xxx√ Tina √xxx

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 SpiderCurlyAceFudgy Dawn xx√x Mark x√xx Josh xxx√ Tina √xxx

Now it’s your turn!!

Sandwiches Sarah, 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?