How to Solve a Logic Puzzle
If you're new to grid-based logic puzzles, this tutorial will teach you the basics. Start with the "Introduction" first, then move on to the tutorials discussing specific clues or solving methods. Each tutorial contains a number of different slides - you can advance to the next slide by clicking "Next slide" at the bottom of each page, or by using the circled numerical links below each slide. Choose your specific tutorial from the list below to get started.
A grid-based logic puzzle can seem daunting if you've never solved one before, but don't get discouraged - once you learn a few basic rules you'll be on your way to completing your first grid in no time. Each logic puzzle is comprised of a list of clues and a grid like the one you see here on your left. The grid will display a certain number of categories (in this case, 4) and a certain number of items per category (in this case, 5). Every item is matched to one, and only one, other item in each category, and no two items in a category will ever be matched to the same item in another category. Your goal is to figure out each item's matches, using just the clues given and pure logical deduction.
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Every puzzle has a set number of categories. In this example, there are four - Prices (green), Names (yellow), Colors (pink) and Zodiac Symbols (blue). Notice how the last two categories (pink and blue) are repeated on both the top and left sides. All logic puzzle grids will follow this same pattern. Why? The point of the logic grid is to determine whether any given item is or is not matched with any other given item. This configuration of categories allows every single item on the grid to intersect with every other item on the grid once, and only once.
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Every item on the grid is labeled on either the left-side or the top-side, or both, depending on the category it is in. In this example there are five items for every category - i.e. Bonita, Daryl, Laura, Mario and Sheila are the five items in the "Names" category. Blue, Green, Orange, Pink and Violet are the five items in the "Colors" category, and so on.
The larger areas where each category intersects are called "subgrids". Each subgrid will always be a square that is outlined in a slightly heavier black line. In this example, the yellow subgrid at the top-left is the Prices-Names subgrid, because it is where the Prices category and the Names category intersects. There are six subgrids total in this sample puzzle.
Every item on the grid has a column (yellow) and/or a row (green) representing it. Each column and row travels across the full-width or full-height of the grid at that point (heights and widths will vary depending on the category). A sub-section of a column or row that is housed entirely within a single subgrid is referred to as either a sub-column (pink) or a sub-row (blue). The smallest squares on the grid, where individual items intersect, are called boxes (purple).
The purpose of the grid is to represent (via boxes) the relationships between every possible combination of every item. Your goal is to fill each of those boxes with either a TRUE marker (green circle) or a FALSE marker (red X), based on your reading of the given clues.
There are two hard rules to always remember in logic puzzles: 1. Every item in the puzzle is matched to one, and only one, other item in each category. 2. No two items in the same category will ever be matched to the same item in another category. Following those two simple rules, check out the four sample subgrids shown to the left. Each of these samples is invalid because it breaks one or both of those rules.
How do you finish a logic puzzle? As you progress through each clue, your task is to translate the relationships described there into TRUE or FALSE markers on the grid. (We'll discuss how to do that starting in the next tutorial). As you proceed through the puzzle, more and more of the grid will be filled in, until all the top subgrids (in this case, there are three) are completely filled in with TRUE markers. At that point, you have successfully revealed the relationships between each and every item on the grid, and puzzle is solved.
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How to Solve a Logic Puzzle
In this tutorial, we will show you how, using logic and clues, you can fill in the logic grid and determine what order the given information should be in.
Play Logic Puzzles
For this tutorial, we shall be using a 3x3x4 grid. This means there are three main squares across the top, as well as three from top to bottom. Inside each square, there is a 4 x 4 grid of smaller squares. These are the squares you will be working with to solve this puzzle. Work along with us by visiting the puzzle:
Solve "Trip to the Doctor"
Let us first start by looking at our information. We have 4 different:
- People: Annabelle, Heather, Kassidy and Tatum;
- Income levels: $54,000, $128,000, $144,000 and $158,000;
- Colored houses: blue, cyan, lime and purple;
- Medications: benazepril, enalapril, fosinopril and ramipril.
Just looking at the information, you might notice that the medication names are all ending in "pril". This is done on purpose to further confuse you while reading clues. You need to be extra careful when you have names that are similar to each other so that you do not accidentally mark the wrong name.
Now, we will look at each clue in the puzzle and show you the corresponding results on the grid table for each clue. You can follow along and by the end, you should have a basic knowledge of how to solve logic grid puzzles! So, let's begin.
The first clue we're given is:
The 4 people were Tatum , the patient who was prescribed enalapril , the employee with the $54,000 salary, and the owner of the purple house.
The first 4 words of the clue tell us one thing: Each piece of information in this clue is a separate person. By that,
- Tatum does not earn $54,000 a year, does not own the purple house and was not prescribed enalapril . (Top, Middle and bottom left boxes);
- The person who earns $54,000 a year is not Tatum , was not prescribed enalapril and does not own the purple house (Top three boxes);
- The purple house owner is not Tatum nor takes enalapril (Second row of boxes);
- The enalapril taker is not Tatum (Bottom box).
Starting in the top left box, we would find the row for $54,000 . We find the box that represents Tatum and $54,000 and place an X inside that box as that combination cannot be true. Tatum does not earn $54,000 . Moving across further, we find where $54,000 lines up with enalapril . As we know, again, that this combination cannot be true, we place an X there, as well. Finally, we place an X where $54,000 meets purple , as the person who earns $54,000 does not own the purple house.
We now move to the second row of boxes. We are concerned here with the purple house. We know that it does not belong to Tatum , so we can place an X where they meet, and likewise, an X where purple meets enalapril .
In the last box, we find enalapril . The only data we can compare with it in this box, are the persons names, and we know it is not Tatum in this case, so we place the final X. You can see the finished grid below.
Clue 2 says:
Of Tatum and Annabelle , one earns $144,000 per year and the other lives in the cyan colored house.
This clue is more complicated than the last clue. At first, you might assume that you can only rule out that the $144,000 salary is not the cyan colored house, because we have no way of knowing, at this point, which of the girls owns the cyan house, and which earns $144,000 . But for now, go ahead and place your X in the $144,000 / cyan combination in the 3rd box on the top row.
Now we can go a little further and rule out that for the $144,000 , it can only be Tatum or Annabelle . Because of that, we can place an X in the $144,000 / Heather combination, as well as in the $144,000 / Kassidy combination, because from this clue we know that neither of those girls earns $144,000 , again, it can only be Annabelle or Tatum . We can do the same in the next box down for the cyan house. Cyan / Heather and cyan / Kassidy cannot be true, so we place our X's.
Clues 3 & 4
The patient who was prescribed enalapril is not Heather .
We place our X in the enalapril / Heather combination in the bottom box.
Either the employee with the $144,000 salary or the employee with the $158,000 salary lives in the blue colored house.
For clue 4, we can figure out that only one of those two salaries can be of the owner of the blue house. Therefore, we can place our X's in the $54,000 / blue and the $128,000 / blue combo's in the third box, top row.
Clues 5, 6 & 7
We're going to look at the next three clues for this section.
Kassidy earns less than Heather .
By this clue, we can use logic to tell us that Kassidy cannot earn the most money, as she earns less than Heather . Likewise, Heather cannot earn the least amount, as she earns more than Kassidy . We can place our X's in Kassidy / $158,000 and in Heather / $54,000 .
The owner of the blue house earns more than Kassidy .
This clue does not help us much at this point. We do not know how much the owner of the blue house earns, nor how much Kassidy earns. We have already determined earlier that the blue house does not earn the least money, so we do not need to place another X. For now, all we know is that Kassidy does not own the blue house. In the second row, first box, we can place an X in the blue / Kassidy combo. We might have to come back to this clue later.
The patient who was prescribed ramipril is not Annabelle .
A simple statement. Bottom box, ramipril / Annabelle combo, place your X. Your grid should now look the same as ours.
Clue 8 (Our first true statement!)
The owner of the lime house was prescribed enalapril for their heart condition.
Now, things will start to get interesting. We finally have a statement that we know to be true. The lime colored house was prescribed enalapril . Because of this, we must do two things. We will first place an O where lime meets enalarpil in the second row, second box.
Because we know that that statement is true, we know that no other colored houses can be combined with enalapril , and we know that no other medications can be combined with the lime house. Therefore, we can X out the rest of the row and column where you placed your O. See the image 5a.
We have our first true combination! Now this is where the grid comes in handy the most. We need to look at the true statement, and find out if we can put any X's, or hopefully O's, into other boxes. Still looking at the top image (5a), find the O and look in the box above it' You will see an X in the $54,000 / enalapril box. We know, therefore, that $54,000 is not enalapril , and so it cannot be lime . The logic is like this: if lime = enalapril and enalapril does not = $54,000 , then $54,000 cannot = lime .
Because of that logic, we can now rule out the $54,000 income belonging to the lime colored house. So, we place our X in the 3rd box on the top row where $54,000 / lime meet. See image 5b.
This leaves us in another interesting situation. Because 3 out of the 4 combinations have been found to be false ( $54,000 is not blue , lime or purple ), that only leaves one more combination. Because of that, it must be true. So now we can place an O for $54,000 / cyan , and add X's to the rest of the column as they cannot be true. ( cyan /128K, cyan / $144,000 which was already x'ed out, and cyan / $158,000 .
Your box should now look like image 5c.
We will use the same procedure as above. Looking at the grid, you have a true condition where $54,000 and cyan meet. In the first box on the top row, we have determined earlier that Tatum does not earn $54,000 , so we know because of that, she also does not live in the cyan house. (Again, if $54,000 = cyan , and Tatum does not = $54,000 , then Tatum does not = cyan . Beautiful logic!)
Because of that, we can put an X in Tatum / cyan . Doing so leaves only one possible combination left for the cyan colored house, and that is cyan / Annabelle . So we also now know that Annabelle owns the cyan colored house. We will place an O there, for true. Image 5d.
Clue 8 Continued...
We will quickly go through the rest of the moves available with this clue.
- You can see you have a true statement in both instances of cyan : cyan = Annabelle , cyan = $54,000 , so Annabelle = $54,000 . True;
- $128,000 is the only income left for Kassidy , therefore it must be true;
- $158,000 is the only income left for Heather . True;
- That leaves Tatum with the $144,000 salary. - Top row, left box is finished;
- In the second row, first box, Kassidy is the only option left for the lime house;
- Because we know Kassidy earns $128,000 , we know that $128,000 = lime house;
- Annabelle earns $54,000 , but enalapril cannot be $54,000 (Top row, 2nd box), therefore, Annabelle cannot be enalapril (Third row). That leaves Kassidy as the only option for enalapril ;
- Kassidy earns $128,000 , and Kassidy = enalapril , so $128,000 = enalapril (Top row, 2nd box);
- We now know one full set: Kassidy earns $128,000 , lives in the lime colored house and takes enalapril !
- Annabelle cannot take ramipril (3rd row), therefore, $54,000 cannot be ramipril ;
- blue is the only house color left for Tatum , so it must be true. (2nd row, 1st box);
- That leaves Heather the purple house;
- $144,000 income ( Tatum , Top row, 1st box) is the blue house, so $144,000 = blue (Top row, 3rd box);
- That leaves purple as the only choice for the $158,000 income. (Top row, 3rd box);
- Cyan cannot be ramipril (Bottom row), so put an X in cyan / ramipril in the 2nd row, 2nd box;
- After all of that, your grid should look like ours for this step.
We have one last clue: The employee with the $144,000 salary was prescribed benazepril for their heart condition.
In the top row, 2nd box, we will set an O (true) for $144,000 / benazepril . After placing our X's, we will see there is only one option left for ramipril , which is the $158,000 income. Set to true.
Fosinopril , which to this point was never mentioned, is the only choice left for $54,000 income. Set true.
At this point, all three boxes on the top row should be filled in completely! We now know all of the answers and do not need to work on the other boxes. (You can still fill them in, if you like.) Your grid should look like ours at this point.
There is nothing left to do now, you have solved the puzzle! The answers are as follows:
Congratulations! You've solved your first logic grid puzzle! Hopefully you weren't too confused by this tutorial! If you have any suggestions as to how we could make it better, please let us know.
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How to Solve Logic Puzzles
Last Updated: June 29, 2021
wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 17 people, some anonymous, worked to edit and improve it over time. This article has been viewed 277,659 times. Learn more...
This article includes general advice for logical reasoning problems, as well as thorough instructions for solving the most common type of logic puzzle. This type of puzzle provides a list or paragraph of clues, then asks you a question that requires you to use the clues to answer. Many books and websites that contain these logic puzzles come with a grid to help you solve them, but this article also includes instructions for making your own.
Setting up a Grid
- Here's an example problem: Three friends named Anna, Brad, and Caroline agree to bring one dessert each to a birthday party. Each friend is wearing a different color shirt. Anna wears a blue shirt. The person who brought brownies couldn't find her red shirt today. Brad didn't bring any dessert at all, which made the person wearing a yellow shirt irritated. Which person brought the ice cream?
- The example question, like all logic puzzles of this type, asks you to match two categories together. You start out knowing the names of several people and the names of several desserts, but you don't know who brought which dessert. Using the clues in the description, you need to figure out how to match each person to a dessert until you know who brought the ice cream. There's actually a third category, shirt color, which should help you get to your answer.
- Note : skip to Using a Grid if the puzzle already comes with a grid set up. Skip to Solving Other Logic Puzzles if your puzzle does not fit this description.
- Write each list separately. When the puzzle mentions a name, add it to a list of names. When the puzzle mentions a color, add it to a separate list of colors.
- Each list should have the same number of items once you've finished. If a list is too short, reread the puzzle carefully for more items.
- Some tricky puzzles will give you hints about what someone doesn't have, such as "Brad didn't make a dessert." In this case, you should add "none" to the list of desserts, which should make it the same length as the other lists.
- For instance, let's say you have three lists. Names : Anna, Brad, Caroline; Desserts : brownies, ice cream, none; and Color of Shirts : red; blue, yellow. Write a vertical list in this order: Anna; Brad; Caroline; (draw a thick line here); brownies; ice cream; none; (draw a thick line here); red; blue; yellow.
- Once you're more familiar with this system, you can get away with not writing every list in both places. We will be using this grid to match items in the vertical list (on the left) to items in the horizontal list (at the top), and sometimes you don't need to match every item. If you've never used this method before, stick with these instructions
- If the list to the left of a section and the list above a section are the same, cross it out. You'll never need to compare the list "Anna, Brad, Caroline" to the list "Anna, Brad, Caroline" – you already know that Anna is Anna.
- Cross out duplicate sections. For instance, the section that compares "Anna, Brad, Caroline" on the left and "red, blue yellow" on the top is the same as the section that compares "red, blue, yellow" on the left and "Anna, Brad, Caroline" on the top. Cross off one of these duplicate sections so you only have one to pay attention to. It doesn't matter which you cross off.
Using a Grid to Solve a Logic Puzzle
- Occasionally, a puzzle cannot be fully solved, meaning you won't be able to fill the entire grid. You should still be able to answer the question it asks.
- If you can't find that square, search the other way around. For instance, find the row labeled "blue" and the column labeled "Anna", instead of the other way around.
- Don't start with a clue that tells you something that doesn't apply, such as "Anna doesn't wear a red shirt." While that's a useful clue that should be marked with an "X", this method will assume you started with a clue that gives positive information.
- In our example, the section that has the clue you just circled compares the names of people to the colors of their shirts. The squares we're crossing off are the combinations we've ruled out, which include Brad or Caroline wearing a blue shirt, and Anna wearing a red or yellow shirt. (Typically, the introduction will tell you that each item can only be matched to one item in each other category.)
- If your puzzle gives you clues about what doesn't match, such as "Anna doesn't wear a red shirt", you should put an X in that column. However, since you haven't found a positive match, you should not cross out any other squares.
- Brad did not bring a dessert. Put a circle in the Brad-none square.
- The person wearing a yellow shirt is not Brad. Put an X in the Brad-yellow square.
- If you're solving a puzzle from another country, look up the names to find out whether they are male or female. Puzzle books that are printed more than 20 years ago will sometimes contain names that were once female, but have now become male (or vice versa).
- The green house comes before another house, so it can't be the last one.
- The black house comes after another house, so it can't be the first one.
- Marcus can't be the one who ran the mile in 6 minutes, no one was ahead of him. Cross out the Marcus-6 square.
- Marcus can't be the one who ran in 8 minutes, because that time is less than 5 minutes behind the one before it. Cross out the Marcus-8 square.
- Either the 15 or 25 minute times would work for this clue. You'll have to wait until more squares are crossed off before you can figure out which time was Marcus's.
- Let's say you've discovered that Caroline wears a yellow shirt. Check the yellow shirt column or row for information in other sections.
- Let's say you notice on your chart that the person with a yellow shirt did not bring ice cream. Because you know that person is Caroline, you can also cross out the square that connects Caroline and ice cream.
- Check Caroline's row or column too and transfer information the same way to the yellow shirt column or row.
- If a row or column within a section has every square crossed off, or more than one square with a circle in it, there was probably a mistake made along the way and you may need to start over.
- If an inconsistency occurs, your guess must have been wrong. Go back to what the chart looked like before you made your guess, and make the opposite one. Always keep track of when you made your guess with a new copy or a different color ink so it's easy to reverse if the guess was wrong.
- If you got the answer without filling out your entire chart, you may not be able to check every clue. As long as your chart doesn't contradict the clues you can check, you are probably correct.
Answering Logical Reasoning Problems
- For example: "A cell phone has fallen down a one foot (30cm) hole. How do you retrieve it? You have a wheel of cheese, three chicken feathers, and a flute." The question is designed to get you thinking about how to use bizarre objects in a creative way, but consider each word and you'll notice the hole is shallow enough to reach down and pick up the cell phone.
- For instance, "A wind is blowing from the east, but you are facing the south side of a tree. Which way are the leaves blowing?" If you don't stop to think, you might have heard "east wind" and automatically answer "east". However, the wind is blowing from the east, so the leaves are actually blowing west.
- For timed tests, if you cannot narrow it down to exactly one answer (or however many the instructions request), you may need to take a guess and move on. Make a note on your notepaper to go back to that question at the end if you have time.
- There are many practice tests available online for free for any major standardized school exam. If you can't find your exact exam, search for practice logic tests that match your education level.
- If the question doesn't give you enough information, make an assumption or estimate and state it clearly. For instance, say "Let's say the skyscraper is 100 stories tall and has 20 windows on each story" or "First, I'll assume everyone is following the speed limit, and then I'll consider what changes if some people are traveling faster."
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Things You'll Need
- Graph paper
- For difficult puzzles, keep track of which clue you used by putting the number of the clue in your grid instead of a circle.  X Research source You may need to add numbers to each sentence of the puzzle description first if the clues do not come in a numbered list. ⧼thumbs_response⧽ Helpful 1 Not Helpful 0
- Some people prefer to keep the duplicate sections when setting up a graph, while others dislike having to keep the same information in two places. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- If you have a spreadsheet program on your computer, you can set up your grid there using the border tool to outline the cells. Then, if you have to choose between two answers (see Step 13), you can simply copy and paste the entire 'solution so far' to another section of the spreadsheet to prove or disprove your guess. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
You Might Also Like
- ↑ http://www.oocities.org/heartland/plains/4484/lptips.htm
- ↑ http://www.psychometricinstitute.com.au/Psychometric-Guide/Logical-Reasoning-test.html
About This Article
To solve logic puzzles, start by rewriting the question to eliminate any unnecessary or nonsensical information. Then, make a list of important clues, such as colors, names, and words that indicate a particular order, like “before” and “after.” If the puzzle is a multiple choice question, check each answer to see if it contradicts something in the question, or if the answer can’t be deduced from the given information. Afterwards, if you’re still stuck, reread the puzzle to see if you’ve missed any clues. To learn more, including how to solve logic puzzles using a grid, scroll down. Did this summary help you? Yes No
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