# Blog

## How to solve a grid-based logic problem

By

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These grid-based logic problems require Sherlock-like deduction! We’ll take you through the basics of solving these tricky word puzzles.

### You will need

• Pencil
• Paper
• Printer (optional)

### A logic problem

Here is an example of a grid-based logic problem. It has three parts: a story, a set of clues and a grid.

Amado, Dan, and Valeria are three friends who are meeting up at the beach. Each one uses a different vehicle: a car, a bike, or a boat. Each vehicle is a different colour: red, green or purple. Using the three clues below, can you work out who arrived in what?

1. Amado’s vehicle is coloured green, but it doesn’t have any wheels
2. The human-powered vehicle is not purple
3. Valeria did not use the red vehicle

### Before you begin

#### 1.

Learn some basic terms of the logic puzzle: category and item. Each puzzle will introduce at least two categories. In this puzzle, there are three categories: friends, vehicles and colours. Each category has several unique items. For example, there are three vehicle items in this problem: car, bike and boat. Can you identify the items in the friend category? The colour category?

#### 2.

Learn the basic rule of logic problems: every item (e.g. boat) is matched to one, and only one, other item in each category. This means that if the boat is matched to purple, the boat cannot be red or green as well. Importantly, this also means that the car and bike can’t be purple – because this colour item is taken by the boat. We’ll use this rule a lot to help us solve the logic problem.

#### 3.

Explore the grid provided with the problem. Each column and row represents one of the items, and each box is the meeting between two of these. You can imagine each box as a true/false question. For example, the purple/boat box is asking “is the boat purple?” We need to write true (O) or false (X) in each box. For example, the picture shows true “is the boat purple”.

#### 4.

Note: our problem’s grid is made up of three sub-tables because we need to compare three sets of category matches: friend-to-vehicle, friend-to-colour and colour-to-vehicle. Each sub-table is a 3×3 because, in this problem, each category has three items. Don’t worry if this seems complicated – just keep reading and we’ll explain along the way.

### 1.

Read the clues looking for matches between items that you can add to your grid. In this problem, the first clue tells us that “Amado’s vehicle is coloured green”. This tells us directly a true match: Amado-green! In your grid, put a “O” in the box for Amado-green to mark it as true.

### 2.

If you mark a true match, mark false in all the remaining boxes in the same row and column of that sub-table. We can do this because of our basic rule: every item is matched to one and only one other item in each category. It’s a powerful rule!

### 3.

Read the rest of the first clue, “…but it doesn’t have any wheels”. This tells us two false matches: Amado did not arrive by bike nor by car because they both have wheels. Mark false in the Amado-car and Amado-bike boxes in our grid.

### 4.

If you mark all but one box as false in a row or a column of a sub-table, the remaining, empty box must be true! In this example, by process of elimination, Amado must have arrived by boat. Mark the box for Amado-boat as true and then because you have marked a box as true, complete Step 2.

### 5.

Here’s a new strategy: Amado took a boat, and Amado’s vehicle was green. So what colour was the boat? It’s obviously green! This strategy is called “transposition”, and it’s a really useful way to fill in empty-looking grids. We can mark the boat-green box as true in the bottom colour-to-vehicle sub-table. Remember to fill in the row and column with false “X” marks!

### 6.

Keep reading clues. The next clue, “The human-powered vehicle is not purple,” gives us another false clue. Mark the box for bike-purple as false. Can you work out which vehicle is purple, and what colour the bike is?

### 7.

The last clue, “Valeria did not use the red vehicle” gives us another false match, which by using steps 2 and 4, allow us to complete the friend-colour sub-table!

### 8.

Finally check for logical transpositions again. This transposition is a little tricker to see but we know we can find one because both colour sub-tables have been solved. So, what do the colours have in common? Red goes with Dan in the top right sub-table, and red goes with the bike on the bottom sub-table. This way, we know Dan arrives on the red bike.

### 9.

By process of elimination, Valeria must arrive in the purple car. Congratulations! Your grid is complete meaning you’ve solved the logic problem!

### More logic problems

Apply the steps above and try your hand at these logic problems!

Problem 1: Allergies

Five friends (Cortez, Erika, Jinlan, Marcus, and Tan) are each allergic to something different: bee stings, cats, nuts, pollen or shellfish. Can you use these clues to match the friend to their allergy?

1. Cortez has a food allergy
2. Erika can play with her kitten for hours without medicine
3. Jinlan’s allergy is not related to animals

Marcus has seasonal allergies

Problem 2: Science fair

The Meza family has three kids named Adriana, Silvia and Carlos. They are all in different years at school: Years 4, 5 and 6. It’s the school science fair and each brings a different experiment: a model dinosaur egg, an electric kite, and a trained rat. Who brought what to which grade level fair?

1. Carlos, the youngest, does not bring an electric kite
2. Adriana was proud of her model dinosaur egg
3. The Year 5 student did not bring the kite either

Problem 3: Dinosaur museum

The local natural history museum is displaying four dinosaurs in four different rooms surrounded by four different habitats. The rooms start with the entry and then are numbered in order of when guests will walk into them. Can you use the clues below to describe each of the exhibits?

1. The first two rooms do not have grass nor a Velociraptor
2. A carnivore lurks in the room right after the Stegosaurus
3. The Apatosaurus is no where near a body of water, but it is in Hall 2
4. The cliff exhibit comes right after the beach exhibit, and it’s not in Hall 2