Logic puzzles are a lot like Ferris wheels: equal parts relaxing, thrilling, and a lot of fun… until you get stuck on one! We all know the frustration of glaring back and forth between the clues and the grid, checking every word and every box, increasingly becoming convinced that the puzzle creator just MUST have made a mistake.
In the interest of brevity, the puzzle solving instructions you’ll find in a printed logic grid puzzle book typically only cover the most basic of techniques to get you started. The aim of this article is to uncover the remaining secrets standing between you and those taunting puzzles that threaten to hasten the ageing process with just a few confounding sentences!
If you take some time now to master the advanced techniques for solving logic puzzles, then together with some brain power (perhaps a coffee or two) you can systematically solve logic puzzles of all levels of difficulty using the puzzle grid.
At the very least, the next time you find yourself stuck on a logic puzzle, the tips outlined below might just get the wheels moving again.
For most of the examples in this article we'll use a simple puzzle scenario where five students are transferring into a new class. The objective would be to determine which subject each student transfers into, the name of the teacher, and the month they transfer into that class.
Note: If you’ve landed on this article and instead need to start with the basics, check out Solving Logic Puzzles For Beginners.
Let’s get started!
1. Advanced Grid Techniques: It’s One Of Two Options
Notice in the circled area of the below example, for the subjects History and Social Studies the subjects have the same two options available to them for Teacher – Mr Duffy and Miss Savage.
Where you see a pattern like this, there is an opportunity to do some additional elimination. And we all know we’re here because we love crossing things out!
Because these two teacher options are going to be shared between the subjects History and Social Studies, we can eliminate those two teacher names for all other subjects, as below:
That’s it for the first tip, a simple one to look out for!
2. Greater Than And Less Than Clues
Consider the following example clue:
Clue: Jonathan transferred classes one month after the Social Studies student, but sometime before Miss Savage's student.
This is the type of clue we’d initially draw some information from, then return to later when we’ve worked through the other clues. But some of that initial information is often missed, so let’s quickly run through what this clue tells us straight away:
- Jonathan can not have transferred classes in the first month available.
- Jonathan can not have transferred classes in the last month available.
- Jonathan is not the Social Studies student.
- Jonathan does not have Miss Savage as a teacher.
- The Social Studies student can not have transferred classes in either of the last two months available (because two students need to come after that person – Jonathan and Miss Savage’s student).
- The Social Studies student does not have Miss Savage as a teacher.
- Miss Savage’s student can not have transferred classes in either of the first two months available.
- Because Jonathan has the next sequential month immediately after the Social Studies student, we can check the grid for any months the Social Studies student has crossed out from other clues. Jonathan can not have the next month after any that are crossed out.
- Vice versa, if we had already crossed out any other months for Jonathan from other clues, we can cross out the month immediately prior to that month for the Social Studies student.
When you have sequential clues like this, it can help to write a quick note to visualize the relationship, i.e.:
Social Studies >(1 month) Jonathan >? Miss Savage
3. Advanced Grid Techniques: Consecutive Fact Pairs
Say we know from the clues that “Andrew transferred classes one month after Amanda” and the below is the state of our grid from other eliminations.
It has been previously determined that Amanda is the student who transferred in either April or May, and that Andrew is the student who transferred in either May or June. If Amanda transferred classes in April, our clue tells us that Andrew will have transferred classes the following month, May. And if Amanda transferred classes in May, then Andrew transferred classes in June.
This situation gives us an additional piece of information – in either scenario, the month of May has to be used by one of these two students, Amanda or Andrew. Therefore, we can eliminate the month of May for all other students:
4. Advanced Grid Techniques: As Above, So Below… And Across
We have touched on this principle in our guide that covers the basic techniques: Solving Logic Puzzles For Beginners, but it is an essential concept to understand in order to fill in every detail you can in a logic puzzle grid!
Tip: Take note of the symmetry in the way we mark information in the grid and you might find these techniques easier to recognize.
Example 1
Take the below partially filled out grid as an example, where we have highlighted the rows and columns we will be looking at:
Anywhere where there is a tick, the information along the row can be transferred to the column below, and vice versa. Why? Using the student “Bella” as an example in the above grid, we know that Bella changed classes in the month of March. So, we can consider any fact about Bella and any fact about the month of March to be one and the same.
Looking at the above grid, we know that the person who changed classes in the month of March did not transfer into Mathematics nor History, and we also know they have the teacher Mr Garcia. All of this information applies to Bella, since we know Bella is the March student, so we can repeat it down Bella’s column as so:
Note where we have just ticked the intersection of Bella and Mr Garcia, the information in the Subject section below – that the subject is not Mathematics nor History – has also been applied to the row, in the section to the right of Mr Garcia’s name.
If you are new to logic puzzles it may seem redundant to mark this information in multiple places, but we do it because one of the sections of facts may have additional information filled in that the other sections don’t have (perhaps not early on, but later as we work through the clues), and this will get us closer to being able to tick more boxes and solve the puzzle.
Example 2
Below we have a similar example, but in this case some of the information in the columns highlighted needs to be marked in the corresponding rows where there is a box ticked, and vice versa – there is information in the rows that needs to be applied to the columns beneath the ticks.
Once we have filled in all the corresponding information, the grid will look like this:
Example 3
So far we have examined transferring the information below or to the right of a ticked box, but we can also deduct more information by looking above or to the left of a ticked box. Take a look at this example, with some areas highlighted:
First, let’s look at the row highlighted yellow, where we know that the teacher who had a student transfer in March is Mr Garcia. Notice that we also know the March student did not transfer into the subjects Mathematics, History, or Social Studies. Given that the March student and Mr Garcia are one and the same, the same subject eliminations apply to Mr Garcia.
Therefore, in the section where Teacher and Subject intersect, we will be able to cross out Mathematics, History, and Social Studies for Mr Garcia.
Looking at the row highlighted in blue, the same principal applies for the April student who we know transferred into Mr Duffy’s class. We know that student is not Toby, Andrew, or Jonathan. Therefore, in the section where Teacher and Student intersect, we can cross out Toby, Andrew, and Jonathan against Mr Duffy’s name.
Finally, in the purple highlighted row we see that Ms Watson has the subject Biology. We also see that Ms Watson does not have students Amanda nor Andrew. So, in the bottom section of the grid where Subject and Student intersect, we can cross out Amanda and Andrew for Biology.
The result of applying all of this information looks like this:
But that’s not all! Take a look at the tick showing Ms Watson has Biology. Travel from there up the Biology column, and you will see a cross indicating that Biology wasn’t the class a student changed to in June. Because Ms Watson and Biology can be treated as one and the same, we can also deduce from this that Ms Watson did not have the June student. We can cross out June for Ms Watson in the far right section where Month and Teacher intersect.
Staying in the section where Month and Teacher intersect, we can see that Ms Watson does not have the March student nor the April student. This information can be transferred to the section where Month and Subject intersect, because we know that Ms Watson is the Biology teacher.
The result of these changes looks like this:
You’ll also notice that thanks to all those eliminations, we now know that Mr Garcia, who has the March student, has the subject Geography. This can be ticked in two sections. But, it’s time for us to move on to the next technique!
5. Unique List Clues
This is a more complex clue type that initially allows you to eliminate a number of options, but can have additional value later once you’ve filled out more of the puzzle.
Clue: The five students are the one who changed classes in March, the one who has Mrs Knight as their teacher, Andrew, the one who has Ms Watson as their teacher, and the student studying Social Studies.
Part 1: The Initial Eliminations
From the information in the clue, we can extract enough information to fill out the grid as above. Why? The clue lists the 5 unique people in the puzzle by referencing one of their attributes. This means that none of the five people are referenced twice in that clue – therefore the other attributes mentioned are immediately ruled out for each person.
For example, we can determine that:
– The student who changed classes in March can not have Mrs Knight nor Ms Watson as a teacher, is not Andrew, and is not studying Social Studies.
– The student who has Mrs Knight as their teacher can not have changed classes in March, can not be Andrew, and is not studying Social Studies.
– Andrew can not have changed classes in March, does not have Mrs Knight nor Ms Watson as a teacher, and is not studying social studies.
And so on.
Is this clue exhausted now? Not necessarily!
Part 2: Revisiting The Clue
Let’s say you have worked through all the clues in the puzzle and have filled out a lot of the grid, but you are a bit stumped. Your grid happens to look like this:
For reference, here is the clue again:
Clue: The five students are the one who changed classes in March, the one who has Mrs Knight as their teacher, Andrew, the one who has Ms Watson as their teacher, and the student studying Social Studies.
Because this clue represents every person in the puzzle, we know that each person is represented by one and only one of those five facts. Knowing this, we can pick out someone from the puzzle and try to determine where they fit into the clue.
In the grid above, take a look at the student named Toby and consider which person he would be in the clue.
- He can’t be Andrew, because we know him by name to be Toby.
- He can’t be the one who changed classes in March, because we know that Toby changed classes in July.
- There is a cross next to Social Studies for his name, so he can’t be the one studying Social Studies.
- The only options left are that his teacher is either Ms Watson or Mrs Knight – however there is a cross next to Mrs Knight for Toby’s column.
- By process of elimination, Toby has to be the person with Ms Watson as a teacher.
Keep looking for more ways to use the information in this clue. For example, if we examine the updated grid:
We can see that there are only two Student name options remaining for the teacher Mrs Knight, who was mentioned in our clue. The options are Amanda and Jonathan. However if we look down Amanda’s column, it shows that she is studying Social Studies – which was also mentioned in our clue. Therefore, Amanda can’t be the one who has Mrs Knight as her teacher, as Amanda has already been covered in the list of students in our clue. Jonathan has to be the student with Mrs Knight as his teacher.
Next, if we take a look at the student Bella, we know that she does not have Mrs Knight or Ms Watson as her teacher, and she is not studying Social Studies, and she can’t be the student named Andrew, so looking at our clue there is only one option that remains – Bella must be the student who changed classes in March.
6. Double Pair Clues
For this example, imagine we have the following clue:
Of the student who transferred in June and the student who transferred to Mrs Knight's class, one had the subject Mathematics and the other was Andrew.
This clue type describes two unique people in the puzzle, we just don’t know which facts match up with each other.
Let’s say we already have some information in the grid from other clues:
The initial information we can get from the clue is that Mrs Knight’s student was not the June transfer, and Andrew did not transfer into Mathematics. We have already made those simple eliminations in the above grid, which have been highlighted.
Once we have been through the other clues in a puzzle and filled some information into the grid, we can return to a clue like this and potentially draw more information from it.
The first recommendation upon returning to this kind of clue is to check if any eliminations have been made that solve how the pairs of facts match up. For example, if June was now crossed out for Andrew, we would know that Andrew must be the one who transferred to Mrs Knight’s class, and that the June student has to be the one who transferred into a Mathematics class. The clue would then be solved.
However if we can’t completely solve the clue yet, we may be able to make further eliminations with this clue type by checking the grid to see if any of these pairs have anything in common. Let’s see the clue again:
Of the student who transferred in June and the student who transferred to Mrs Knight's class, one had the subject Mathematics and the other was Andrew.
Firstly, if there are any facts we’ve already determined about both the June transfer and Mrs Knight that they share, we can apply the same information to both the subject Mathematics and Andrew (they are the same two people, we just don’t know which is which). The above grid does not have any information that helps with this scenario though.
Now let’s look at the second half of the clue – are there any facts in the grid shared between both Andrew and Mathematics? They both have the months March and July crossed out! This means we can also cross out these months for Mrs Knight, because she is the teacher of either Andrew or the student who transferred into Mathematics.
It might be easier to digest this reasoning in simple logic statements:
- Mrs Knight matches to either Andrew or Mathematics
- Neither Andrew nor Mathematics match to March or July
- Therefore Mrs Knight does not match to March or July.
Additionally, the grid shows that Andrew did not transfer into Geography or Social Studies. The clue tells us that the June student and Mrs Knight’s student are Andrew and the Mathematics student (without knowing which is which) – so we can extrapolate that neither the June student nor Mrs Knight’s student transferred into Geography or Social Studies.
The above findings allow us to make these grid eliminations:
7. Looking For Elimination Patterns
This is another fun pattern to look out for! Take a look at the below example and see if you can deduce an additional elimination we can make.
As displayed in the grid, previous eliminations show us that we know Bella’s month is either March or April. We also know that Biology’s month is not March nor April.
This tells us that Bella and Biology can not possibly share any of the month options, therefore we can determine that Bella can not be the student who transferred into the subject of Biology, and we can put an X in the grid where Bella and Biology intersect.
Of course, in the real world you’re going to be studying a grid that has many more markings than this simplified example, and it can take some time to spot these patterns.
Here’s a more complex example:
- Based on available Month options, we can see that Toby can not be the student who transferred into Geography (The geography transfer was in either March or May, but Toby has both those months crossed out).
- As previously determined, Bella can not be the Biology student (we’ve crossed this out already).
- The month of April is either Mathematics or Social Studies. Looking at where Teachers and Subjects intersect, we can see that Mr Garcia and Miss Savage both have both those subjects crossed out, therefore neither of those Teachers can match to the month of April.
- Again, the month of April is either Mathematics or Social Studies. Looking down Toby’s column, we can see he has both those subjects crossed out. Toby can not be April.
- Where Subject and Student intersect, we can see that Geography is either Toby or Bella. Where Month and Student intersect, we can see that May is crossed out for both Toby and Bella. Therefore, May can not match to Geography.
8. Sometimes You Need To Take Notes
Some harder puzzles get so complex that unless your brain is as sharp as a surgeon’s scalpel, you’re going to need to take notes.
Consider the following set of clues:
- Andrew transferred classes one month before Ms Watson’s student.
- The Social Studies student changed classes one month after Mr Garcia’s student, but one month before Jonathan.
- Toby changed classes sometime after the Mathematics student, who changed classes sometime after Bella.
- The History student changed classes one month before the Biology student.
Some simple scribbles that lay out the order of each group of facts should help you visualize which consecutive arrangements can and can’t work.
9. Trial And Error Is OK Too !
One thing you can rely on with a logic grid puzzle is that there is only a single solution, and it can be arrived at entirely with logic – no guesswork.
But if you’re stuck, it is okay to test out a possible solution and see if it works – this is a form of logical deduction in itself!
Ready to give a hard logic puzzle a try? Here are a few to choose from: