This guide is suitable for beginners, or the experienced who are in need of a refresher.
This article contains a detailed walkthrough of solving a logic puzzle step by step. You may prefer to read our shorter guide How To Solve A Logic Puzzle which outlines the basics of how to use our free interactive logic puzzles online.
Introduction
Also referred to as cross logic puzzles or logic problems, logic grid puzzles are an enjoyable workout for the brain that can range from relatively easy to mind-bendingly difficult!
There are many varieties of logic puzzles and problems, but these instructions are designed to teach you how to solve the type of logic puzzles that come with a grid to fill in as you work through the clues. You might also know these as matrix or table logic puzzles. This grid visualizes all the dimensions of the puzzle and helps you work towards the solution.
Logic grid puzzles begin with a brief story introducing the scenario. It’s helpful to read this, but particularly if you get stuck – sometimes extra information you need is mentioned in the scenario.
There will also be a set of clues, and several groups of answers. Your job is to determine the correct relationships between the groups of answers, and marking out the provided grid with ticks and crosses helps you get to the solutions.
Read each clue carefully! It is very common that more than one piece of information will be revealed from a single clue.
As a quick example of a logic puzzle’s typical format, you might be given a scenario where five people each take their pets to a vet on a particular day, each having different appointment times. You are told the five names of the people, the five pet names, and the five appointment times. It is then up to you to work through the clues given to determine which person (identified by their name) owns which pet, and what their appointment time is.
Note that relationships are always unique – in the above vet example, it can be assumed that every one of the names and appointment times will be used and no detail will be used more than once.
Most puzzles show a difficulty rating. In harder puzzles, clues can get quite complex and are often interdependent on other clues. It’s a lot of fun if you enjoy practicing problem solving skills!
Logic Puzzle Example
In order to delve further into how to solve a logic puzzle we’ll use a small, easy puzzle as an example. This is a very simple logic puzzle – you will usually see them larger with more clues and complexity. If you would like to print a copy of the grid to use to follow along, click here to download the file as a PDF. Alternatively, you can do the puzzle on our website.
Puzzle Description: Lucy is a sought-after cake maker in the friendly small town of Plumpton. There aren't enough residents in the town to run her business full-time, so she bakes and decorates the cakes in the evenings after her main job. Tomorrow night, Lucy will be busy with three cakes to prepare - all different flavors and occasions! From the clues given, can you determine which client (identified by first name) ordered which type of cake, what the occasion is, and the price each customer will pay?
Below is the grid that would be provided with this puzzle. Note that the grids shown in this article are only images for illustrative purposes and are not interactive grids you can click on.
This puzzle has four (4) factors, or sets of facts – Name, Flavor, Occasion, and Price. Each factor has three (3) options. Consequently this would commonly be referred to as a 4 x 3 puzzle. You don’t need to know this, but you will often see this notation describing a logic puzzle so it’s helpful to understand what it means.
The grid is laid out in such a way that the relationship or intersection between each set of factors is shown once.
Clues 1. Emma ordered carrot cake for an event she is hosting at her home, but it did not cost $37.00. 2. Attendees of the farewell party will each be enjoying a big slice of vanilla cake. 3. The cake Michael ordered cost $2.00 less than the cake that is for a birthday. 4. The chocolate cake is Lucy's specialty, which she currently has discounted to $35.00.
Clue 1 tells us two pieces of information. First, that Emma ordered carrot cake. We can now tick the box that intersects between “Emma” and “Carrot” in the grid. Additionally, we can cross out Carrot as a flavor for the other two names, because we know that Emma is the one with the Carrot cake. We can also cross out the Chocolate and Vanilla cake flavors for Emma, since we know hers is the Carrot.
Note that if you are doing a logic puzzle on an app or website like ours, when you tick a box the adjacent column and row crosses will be filled in for you automatically.
The second part of Clue 1 tells us that Emma did not pay $37.00 for her cake. This allows us to cross out $37.00 in the grid against Emma’s name, and because we know that the Carrot flavor cake is Emma, we can cross out $37.00 where it intersects with Carrot.
Clue 2 tells us that Vanilla flavor is for the occasion of a Farewell Party. This is a simple case where we can tick the box corresponding between these two details, and cross out the values in the row and column around it.
Clue 3 is a little more complex. “The cake Michael ordered cost $2.00 less than the cake that is for a birthday.” This is the kind of clue that will initially tell us a few details, but we will need to come back to it again later once we have more of the grid filled in.
Firstly, this clue tells us that Michael’s cake is not the Birthday cake (as his cake cost less than the birthday cake). We can put a cross in the grid where “Michael” intersects with “Birthday”.
Secondly, the clue tells us that Michael’s cake can not be the most expensive cake. So we can cross out the $39.00 price for Michael.
Thirdly, the clue tells us that the Birthday cake (which costs more than Michael’s cake) can not be the cheapest cake. So we can cross out the $35.00 price for the Birthday occasion.
Here’s what this looks like:
Clue 4 is the final clue, and it tells us that the chocolate cake cost $35.00. We can tick that in the grid, and as always cross off the options in the same row and column of that section.
Now it’s time to do some work in the grid without referencing any clues!
In the grid just shown, take a look at the area where Price and Flavor intersect. There is only one price left that Carrot can be, so we can tick $39.00 for Carrot. After doing so, there is only one Flavor remaining that can be $37.00: Vanilla. We can tick that box, and we now have our first complete section.
There’s more we can do. Wherever you have placed a tick, the values in other sections along the same row also apply to the column below the tick. For example, looking at the grid above, Emma has the Carrot flavor – and if we run our eyes along Emma’s row beyond the Flavor section, we can see that the Price of $37.00 is crossed out for Emma. Since we can consider Emma and the Carrot flavor as one and the same, we could then look down the Carrot column and cross out $37.00 there as well, but in this case it has already been done.
If we look down the Carrot column though, we can see that the price of $39.00 has been determined for that Flavor, and that this cake is not for a Farewell Party. This information can also be applied to Emma’s row, as shown:
Now we’ll look for another tick where the information further on in the row can be applied in the column below the ticked square (and vice versa).
Where the Price of $35.00 is ticked for the Chocolate Flavor, further across the $35.00 row it shows that the $35.00 cake is not for a Birthday Occasion. Therefore, the same is true for the Chocolate Flavor. We can follow down the Chocolate column and cross off Birthday, as below:
Now we have only one Occasion option for the Chocolate Flavor – it must be for a Graduation. We can also see that the Birthday cake must be a Carrot Flavor cake.
We now know all the Prices for each Flavor, and we know all the Occasions for each Flavor. From this information, we can fill in all the Prices for each Occasion. For example, we can see that the Chocolate Flavor is $35.00, and that the Chocolate Flavor is for a Graduation. So, we can tick where $35.00 and Graduation intersect. We can do this for all Price/Occasion combinations.
Clue 3, which we had to come back to, was “The cake Michael ordered cost $2.00 less than the cake that is for a birthday.” Now that we know the exact Price of the Birthday cake ($39.00), we can determine that the Michael’s cake is $37.00.
This leaves only one option for the Price of Sally’s cake, so we can tick $35.00 for Sally.
We’re now at the point where all our clues have been exhausted, but we still don’t appear to have a complete solution. What else can we do in the grid?
Notice that we have all the Prices figured out for Flavors, and we also have all the Prices determined for Names. We can use this information to match up Flavors with Names! For example, the Chocolate cake was $35.00, and Sally’s cake is $35.00, so in the first section we can tick that Sally has the Chocolate cake. We can use the same method to determine that Michael has the Vanilla cake. Now, we have progressed to this point:
All that is left now is to cross reference information we already have in the grid to determine the remaining Name and Occasion combinations. We can see that Sally’s cake is $35.00, and the Graduation cake is $35.00, therefore Sally’s cake is the Graduation cake. This means there is only one square left to tick – Michael’s cake has to be for a Farewell Party!
Most logic puzzles additionally come with a table to enter your answers in a simplified easy to read form. If you are using an app or a website, this information will be filled in for you automatically. In a book, you can write it in if you want to. It makes it easier to check against solutions too.
While this was an easy example, we’ve covered the basic concepts and you should now be able to attempt some easy puzzles using the lessons you’ve learned in this tutorial. We’ll be covering more advanced techniques and clue types in our next article!
Ready to have a go at solving a logic grid puzzle? Try our ‘Very Easy’ rated puzzle: Daycare Dropoffs.
Prefer to learn some more skills first? Read our article Advanced Logic Puzzle Techniques.