How to Solve Logic Puzzles: Using the Grid, Step by Step

Here's how to solve logic puzzles of the classic grid kind: set up a grid that compares every category against every other, mark an X for each pairing a clue rules out and an O (or a check) for each pairing you prove, and after every new mark, follow the consequences through the rest of the grid. Every clue is a fact, and the answer is the only arrangement that makes all the facts true at once. You never need to guess.

This guide shows you exactly how to do that. We'll build the grid, go through each kind of clue (direct, either-or, comparison and "neither" clues), work through a full puzzle one deduction at a time, and look at the famous 1962 "zebra puzzle," often called Einstein's riddle. There's also a small practice puzzle with its answer.

What a Logic Grid Puzzle Is

A logic grid puzzle (sometimes called a logic problem or a matching puzzle) gives you a short story, a few categories of things, and a list of clues. For example: four friends, four puzzle types and four finishing times. Each friend did exactly one puzzle and finished in exactly one time. Your job is to match everything up.

Three rules hold in almost every puzzle of this type:

• One-to-one matching. Each item in a category goes with exactly one item in each other category. No two friends did the same puzzle.
• The clues are all true. There are no trick clues and no lies, unless the puzzle says otherwise.
• There is exactly one solution. A well-made puzzle can be solved by pure reasoning. If you find yourself needing to guess, you've missed a deduction somewhere.

Why it's called deduction

Philosophers separate two kinds of reasoning. In a deductive argument, true premises guarantee the conclusion. In an inductive one, the premises only make the conclusion likely. The Internet Encyclopedia of Philosophy's article on deductive and inductive arguments, by Timothy Shanahan of Loyola Marymount University, gives the textbook example: if all men are mortal and Socrates is a man, Socrates must be mortal. The Stanford Encyclopedia of Philosophy's entry on logical consequence (by Jc Beall, Greg Restall and Gil Sagi) describes the same idea as the premises being necessarily sufficient for the conclusion.

Logic grid puzzles are pure deduction. Every X you write must follow with certainty from the clues and from marks you've already proven. That's what makes them satisfying: when you're done, you don't just have an answer, you know it can't be anything else.

Setting Up the Grid

The grid is a set of small square tables, one for each pair of categories. With three categories (say People, Puzzles and Times), you need three pairings:

• People against Puzzles
• People against Times
• Times against Puzzles

Printed puzzles usually arrange these as a staircase: the first category runs down the left side, the other two run across the top, and the third category also runs down the left under the first. You get an L-shaped block of squares. The layout doesn't matter as long as every pair of categories has its own table.

The number of pair-tables grows quickly as categories are added. With k categories you need k × (k − 1) ÷ 2 tables. Here's what that means in practice, assuming each category has n items, so each table has n × n cells:

Categories	Items per category	Pair-tables	Total cells
3	3	3	27
3	4	3	48
4	4	6	96
4	5	6	150
5	5	10	250
6	5	15	375

The arithmetic is simple: tables = k(k − 1)/2 and cells = tables × n × n. For four categories of four, that's 6 × 16 = 96 cells. For the zebra puzzle we'll meet later, with six categories of five items (houses, colors, nationalities, drinks, pets and a fifth trait), a full grid would have 15 × 25 = 375 cells, which is why people usually solve that one with a different kind of chart.

X, O and checkmarks

Use an X for "definitely not" and an O (or a check, or a filled dot) for "definitely yes." Write nothing in a cell you haven't proven either way. Never mark a cell because something "seems likely."

Some solvers also keep a short list of side notes next to the grid, such as "Ben = sudoku + 5 minutes." Those notes hold information that the grid can't show directly, especially comparison clues.

The Three Rules That Do Most of the Work

Most beginners read a clue, mark one X, and move on. Experienced solvers squeeze every mark for all it's worth. These three rules are where the real solving happens.

Rule 1: An O clears its row and column

When you place an O, every other cell in that row and that column of that small table becomes an X. If Ana did the crossword, nobody else did the crossword, and Ana did nothing else. That single O can produce six X's in a 4 × 4 table.

Rule 2: The last empty cell is an O

If a row in a small table has an X in every cell except one, the remaining cell must be an O. Same for columns. This is the grid version of "it has to be somebody."

Rule 3: Carry facts across tables (transitivity)

This is the one people miss. If you know Cara did the sudoku, and you also know the sudoku took 10 minutes, then Cara took 10 minutes. Mark it in the People-Times table. And the reverse works for X's: if Cara did the sudoku, and you know the sudoku did not take 25 minutes, then Cara did not take 25 minutes.

In general: whenever you have an O linking two items, everything you know about one of them (its O's and its X's in other tables) transfers to the other. After every O, check every other table for facts to carry over.

Clue Types and How to Mark Them

Logic puzzle clues come in a handful of recurring shapes. Recognizing the shape tells you exactly what to mark.

Clue type	Example	What you can mark
Direct yes	"The word search took 20 minutes."	O at word search / 20, then clear its row and column.
Direct no	"Dev didn't do the crossword."	X at Dev / crossword.
Compound no	"Cara didn't do the maze, and she finished before Dev."	X at Cara / maze; Cara and Dev are different people, so mark nothing linking them, but note the comparison.
Comparison	"The crossword took longer than the maze."	Crossword can't be the shortest time; maze can't be the longest; and they're different items.
Exact difference	"Ben finished 5 minutes after the sudoku solver."	Ben didn't do the sudoku; Ben can't have the shortest time; the sudoku can't have the longest time.
Either-or	"Either Ana did the crossword or Ana took 10 minutes, but not both."	Exactly one of the two is true. If you later prove one, the other is false, and vice versa.
Neither-nor list	"The four people are Ana, the maze solver, the person who took 10 minutes, and Dev."	All four descriptions are different people, so mark X between each pair.

Comparison clues hide extra X's

A clue like "the crossword took longer than the maze" gives three facts, not one. With times of 10, 15, 20 and 25 minutes:

• The crossword can't be 10 minutes, because nothing is shorter than 10.
• The maze can't be 25 minutes, because nothing is longer than 25.
• The crossword and the maze are different puzzles (obvious here, but with people, "Cara finished before Dev" tells you Cara isn't Dev, which matters in clues that describe people by what they did).

Exact-difference clues hide even more

"Ben finished 5 minutes after the sudoku solver" means Ben's time is one step up from the sudoku's time. So Ben can't be 10 (there's no time 5 minutes earlier), the sudoku can't be 25, and Ben didn't do the sudoku. Later, when you learn the sudoku's time, you'll instantly know Ben's.

Either-or clues: the "not both" matters

Read either-or clues carefully. "Either A or B, but not both" is called an exclusive or: exactly one is true. Some puzzles only say "either A or B," and printed puzzle conventions vary on whether both can be true. When the puzzle spells it out, as most do, use it. Either way, an either-or clue about two different descriptions often tells you those two descriptions belong to different people.

How to Solve Logic Puzzles: A Full Worked Example

Let's put it all together. We wrote this puzzle ourselves, so the people in it are illustrative, and we checked with a short computer search that it has exactly one solution.

Four friends, Ana, Ben, Cara and Dev, each solved one puzzle at a puzzle night: a crossword, a sudoku, a word search and a maze. Each finished in a different time: 10, 15, 20 or 25 minutes.

1. Ben finished 5 minutes after the person who did the sudoku.
2. Cara didn't do the maze, and she finished faster than Dev.
3. The word search took 20 minutes.
4. Either Ana did the crossword or Ana finished in 10 minutes, but not both.
5. Dev didn't do the crossword.
6. The crossword took longer than the maze.

Set up three 4 × 4 tables: People/Puzzles, People/Times and Times/Puzzles. Then follow along.

First pass: the easy marks

• Clue 3: O at word search / 20. Clear the row and column: the word search isn't 10, 15 or 25, and 20 isn't the crossword, sudoku or maze.
• Clue 1: Ben didn't do the sudoku (X). Ben isn't 10 minutes (X). The sudoku isn't 25 minutes (X).
• Clue 2: Cara didn't do the maze (X). Cara finished faster than Dev, so Cara isn't 25 (X) and Dev isn't 10 (X).
• Clue 5: Dev didn't do the crossword (X).
• Clue 6: The crossword isn't 10 (X). The maze isn't 25 (X).

Snapshot: the Times/Puzzles table after the first pass

It helps to see what the grid looks like at this point. Here's the Times/Puzzles table with every mark from the first pass, including the X's that came from clearing the word search's row and column. A dash means the cell is still blank.

Time	Crossword	Sudoku	Word search	Maze
10 min	X (clue 6)	-	X	-
15 min	-	-	X	-
20 min	X	X	O (clue 3)	X
25 min	-	X (clue 1)	X	X (clue 6)

Look at the bottom row. Three of its four cells are X's. That's Rule 2 waiting to happen, and it's exactly the kind of nearly finished row you should scan for after every pass. In the People/Puzzles table, meanwhile, we have just three X's (Ben/sudoku, Cara/maze and Dev/crossword), and in the People/Times table three more (Ben/10, Cara/25 and Dev/10). Those look scattered now, but they all come into play within the next few steps.

Deduction 1: Which puzzle took 25 minutes?

Look at the 25-minute row of the Times/Puzzles table. The word search is out (it's 20). The sudoku is out (clue 1). The maze is out (clue 6). Only the crossword is left, so by Rule 2, the crossword took 25 minutes. Put an O there and clear its row and column.

Deduction 2: Who did the crossword?

Dev is out (clue 5). Cara isn't 25 minutes (clue 2), and the crossword is 25 minutes, so by Rule 3 Cara didn't do the crossword. That leaves Ana or Ben.

Could it be Ben? Then Ben took 25 minutes, and by clue 1 the sudoku took 20. But 20 minutes is the word search. That's a contradiction, so Ben didn't do the crossword. Ana did the crossword, in 25 minutes.

Check clue 4: Ana did the crossword, and she didn't take 10 minutes. Exactly one part is true, so clue 4 is satisfied.

This step used a short "what if" chain. That's fine and fully logical, as long as you follow a supposition all the way to a contradiction. It's not guessing: you're proving a cell must be X because the alternative breaks a clue.

Deduction 3: Ben's options

Now Ben, Cara and Dev share the sudoku, word search and maze, and the times 10, 15 and 20. The sudoku can't be 20 (that's the word search) or 25 (that's the crossword), so it's 10 or 15. By clue 1, Ben is 5 minutes more: either 15 or 20.

• If the sudoku took 15, Ben took 20, so Ben did the word search. Then Cara and Dev share the sudoku (15) and the maze (10). Cara can't do the maze (clue 2), so Cara does the sudoku at 15 and Dev does the maze at 10. But Dev can't be 10 (clue 2). Contradiction.
• So the sudoku took 10, and Ben took 15.

Deduction 4: Wrap it up

Ben took 15 minutes. That's not the sudoku (10) or the word search (20), so Ben did the maze in 15 minutes. Cara and Dev share the sudoku (10) and the word search (20). Dev can't be 10, so Dev did the word search in 20 minutes and Cara did the sudoku in 10 minutes. Check clue 2: Cara (10) finished faster than Dev (20). Yes.

Person	Puzzle	Time
Ana	Crossword	25 minutes
Ben	Maze	15 minutes
Cara	Sudoku	10 minutes
Dev	Word search	20 minutes

Always check every clue at the end

Run down the list one more time. Clue 1: Ben (15) is 5 minutes after the sudoku (10). Clue 2: Cara didn't do the maze, and 10 is faster than 20. Clue 3: word search, 20. Clue 4: Ana did the crossword and didn't take 10. Clue 5: Dev did the word search. Clue 6: crossword (25) is longer than maze (15). All six hold. Checking takes thirty seconds and catches the occasional slip.

Strategies for Harder Puzzles

Bigger puzzles use the same moves, just more of them. These habits make the difference.

Re-read every clue after each breakthrough

A clue that told you nothing at the start can become decisive later. In our example, clue 1 gave only a few X's on the first pass, but it cracked the puzzle once we knew the crossword's time. Make a habit of sweeping through all the clues every time you place an O.

Look for the most restricted item

Scan the grid for any row or column with only two empty cells. Those are the places where a single new fact finishes the job, and they're the best targets for a "what if" test.

Test a supposition only to a contradiction

When you're stuck, pick a two-option cell and ask, "If this were true, what would follow?" Follow the chain until you either reach a contradiction (so the cell is X) or run out of consequences. If you run out without a contradiction, erase everything from that test. The supposition wasn't proven, so neither are its consequences. Using a different color pencil for suppositions makes this easy.

Track ordered categories on a number line

Times, ages, prices in puzzles, house positions and finishing places are ordered. For clues like "two places after" or "somewhere left of," a quick sketch of the slots (1 2 3 4 5) with possible positions written in is often clearer than the grid.

Watch for hidden "different person" facts

Clues like "The four people are Ana, the maze solver, the person who took 10 minutes, and Dev" say that four descriptions all belong to different people. That's six separate X's in one sentence. Comparison clues ("Cara finished before Dev") also quietly tell you two descriptions are different people.

Einstein's Riddle: The 1962 Zebra Puzzle

The most famous logic puzzle of all is the "zebra puzzle," often credited to Albert Einstein, though there's no evidence he wrote it. The version people usually quote ran in Life International in 1962. A page hosted at Florida State University, "Who Owns the Zebra?", reproduces it with 14 clues and notes that its author remembered it from the international edition of Life in 1962.

The setup: five houses in a row, each a different color, each home to a person of a different nationality who keeps a different pet, drinks a different drink and smokes a different brand of cigarette (a period detail). Clues include facts like "the Norwegian lives in the first house," "the person in the middle house drinks milk," and "the green house is immediately to the right of the ivory house." The two questions are: who drinks water, and who owns the zebra? Neither water nor the zebra is mentioned in any clue, which is part of the fun.

How to approach it

A full grid for six categories of five would need 375 cells, so most solvers use a different chart: five columns for the five houses, and a row for each category. You fill in each column as you learn what's in that house. Position clues ("next to," "immediately to the right of," "the middle house") work well on this layout.

The fixed-position clues go in first: the Norwegian in house 1 and milk in house 3. The Norwegian lives next to the blue house, so house 2 is blue. The green-ivory pair has to sit side by side, which leaves only a few places it can go. From there it's the same game of X's, O's and short "what if" chains.

The answer

We solved the puzzle by computer search to confirm it has exactly one solution. Spoiler ahead: the Norwegian, in house 1, drinks water, and the Japanese resident, in house 5 (the green house), owns the zebra. If you'd like to solve it yourself first, the FSU page has the full clue list.

Why computer scientists love it

The zebra puzzle is a classic example of a constraint satisfaction problem, a type of problem studied in computer science courses. University of Waterloo lecture slides by Pascal Poupart (CS486/686, Lecture 4: Constraint Satisfaction) define such a problem as a set of variables, a domain of possible values for each, and a set of constraints that say which combinations are allowed. Clearing rows when you place an O is a version of what the slides call constraint propagation, and "what if" testing is a version of backtracking. When you solve a logic grid by hand, you're running the same ideas a computer would, just with a pencil.

A Little History of Logic Puzzles

Puzzles built on pure reasoning go back a long way. Lewis Carroll, the Oxford mathematician who wrote Alice's Adventures in Wonderland, published The Game of Logic, dated 1886 in the Project Gutenberg edition. It teaches syllogisms (two premises leading to a conclusion, like the Socrates example) with a diagram divided into compartments and nine counters, red ones for "something is here" and gray ones for "this is empty." The premises are playful: new cakes, nice cakes and wholesome cakes, or dragons that are uncanny and Scotchmen who are canny, from which you work out that no dragon is a Scotchman. It's a direct ancestor of today's grids, which also work by marking what's occupied and what's ruled out.

The story-and-clues format grew up in magazines and puzzle books, and the 1962 zebra puzzle is its most famous early example. Today the same format, with its grid of X's and O's, appears in puzzle books, newspapers, apps and classrooms.

Try It Yourself: A Practice Puzzle

Here's a small three-by-three puzzle we wrote and checked for a unique solution. The people are illustrative.

Kim, Lou and Max sit in seats 1, 2 and 3 (left to right) and each brought one snack: an apple, a bagel or some cheese.

1. The bagel is in seat 1.
2. Max sits immediately to the right of Kim.
3. Lou didn't bring the bagel.
4. The apple isn't in seat 3.

Hint: start with clue 2 and list the only two ways Kim and Max can sit.

Solution: Clue 2 allows Kim 1 and Max 2 (Lou 3), or Kim 2 and Max 3 (Lou 1). In the second arrangement, Lou is in seat 1 with the bagel, which breaks clue 3. So Kim is in seat 1 with the bagel, Max is in seat 2 and Lou is in seat 3. The apple isn't in seat 3, so Max has the apple and Lou has the cheese.

Other Kinds of Logic Puzzles

Grid puzzles are only one branch of the family. The same deductive habits (mark only what's proven, follow consequences, test suppositions to a contradiction) carry over to many other puzzle types.

Puzzle type	What you deduce	Key skill it shares with grid puzzles
Logic grid (matching)	Which items go together across categories	X-and-O elimination and transitivity
Ordering or seating puzzles	Who sits or finishes in which position	Number-line sketches for "left of" and "two places after" clues
Truth-tellers and liars	Who is telling the truth	Testing a supposition until it contradicts itself
Sudoku	Which digit goes in each cell	"Last empty cell" logic and candidate elimination
Syllogisms	What conclusion follows from two premises	Pure deduction from stated facts

A quick truth-teller puzzle

Here's a classic style of puzzle to show how supposition testing works outside a grid. On an island, knights always tell the truth and knaves always lie. You meet two islanders, A and B. A says, "We are both knaves." What are they?

Suppose A is a knight. Then A's statement is true, so A is a knave. That contradicts the supposition, so A must be a knave. A knave's statement is false, so "we are both knaves" is false. Since A is a knave, B can't also be one. A is a knave and B is a knight. It's exactly the same move as Deduction 3 in our worked example: assume, follow, hit a contradiction, conclude.

How to Write Your Own Logic Puzzle

Making a logic puzzle is a great way to understand how they work, and it's a fun challenge for students. Here's the process we used for the worked example above.

1. Pick the answer first. Decide the full solution table before writing a single clue. For a first puzzle, three categories of three or four items is plenty.
2. Write a mix of clue types. Include one or two direct clues as footholds, then add comparison, exact-difference and either-or clues. Every clue must be true of your answer.
3. Solve it yourself, cold. Put the answer away and solve from the clues alone, writing down each deduction. If you reach a point where two answers both still fit every clue, the puzzle isn't finished. Add a clue that separates them.
4. Remove extra clues. Try deleting each clue in turn. If the puzzle still has only one solution without it, the clue is optional. Removing a few makes the puzzle harder and more elegant; keeping a few makes it friendlier.
5. Test it on someone else. A fresh solver will spot ambiguous wording, like an "or" that could mean "or both."

When we built the practice puzzle in this guide, our first draft allowed two different answers, so we added clue 4 ("The apple isn't in seat 3") to make the solution unique. That's normal. Nearly every puzzle needs a round or two of adjustment.

Common Mistakes

• Marking a guess as a fact. If a cell isn't proven, leave it blank. One unproven O can poison the entire grid.
• Forgetting to clear after an O. Every O should be followed by X's across its row and down its column.
• Not transferring facts between tables. Rule 3 is where most stuck solvers find their missing step.
• Misreading comparison direction. "Finished faster" means a smaller time; "finished after" means a larger time. Underline these words.
• Treating "or" loosely. Check whether an either-or clue says "but not both."
• Skipping the final check. Re-read every clue against your answer before you call it done.

Logic Puzzles in the Classroom and Beyond

Grid puzzles work well for groups because the reasoning can be said out loud: "Ben can't be 10 because he's 5 minutes after someone." That makes them a good fit for puzzles for classroom centers and puzzles for early finishers, where students can work in pairs and explain each mark to each other. Start younger solvers on three-by-three puzzles with direct clues, then add comparison and either-or clues.

If you enjoy the elimination side of logic grids, you'll probably like number-placement puzzles too. Sudoku uses the same "last empty cell" idea, and techniques like naked pairs in sudoku are close cousins of grid deduction. See our sudoku strategy guide and the roundup of games like sudoku for more. And for what the research does and doesn't say about puzzles and thinking skills, read are puzzles good for the brain.

Wrap-Up: Make a Puzzle Page of Your Own

Solving logic puzzles comes down to a few steady habits: build the grid, mark only what's proven, clear rows and columns after every O, carry facts between tables, and re-read the clues after each breakthrough. If you're putting together a puzzle night or a classroom packet, our free puzzle maker lets you type your own words or pick a theme, choose a puzzle type, and print it with an answer key, so you can pair a homemade logic problem with a word puzzle or two.

Five Habits for Harder Grid Puzzles Compared

Bigger puzzles use the same moves, just more of them. This table compares five habits that make the difference.

Habit	What to do	Why it helps
Re-read every clue	Sweep through all the clues every time you place an O	A clue that told you nothing at the start can become decisive later
Find the most restricted item	Scan for any row or column with only two empty cells	A single new fact finishes the job there, and these are the best targets for a "what if" test
Test a supposition	Pick a two-option cell and follow the chain until you reach a contradiction, then erase everything from that test if you don't	An unproven supposition doesn't prove its consequences, and a different color pencil makes this easy
Use a number line	Sketch the slots (1 2 3 4 5) for ordered categories like times, ages and finishing places	Clues like "two places after" or "somewhere left of" are often clearer than in the grid
Watch for "different person" facts	Notice when a clue lists several descriptions or compares two people	One sentence can give several X's, such as six from four descriptions that all belong to different people

Frequently Asked Questions

What is the first step in solving a logic grid puzzle?

Set up the grid so every category is compared with every other category, then read through all the clues once and mark the easy facts. Direct clues like "Dev didn't do the crossword" become X's, and direct yes clues become O's. After each O, clear the rest of its row and column with X's. Only then start looking for deeper deductions. That first pass usually fills a surprising share of the grid and shows you which rows are nearly finished, which is where the next breakthrough tends to come from.

What do X and O mean in a logic puzzle grid?

An X means a pairing is definitely ruled out, such as "Ana did not do the maze." An O, a check or a filled dot means a pairing is definitely true, such as "Ana did the crossword." Leave a cell blank when you haven't proven it either way. Because each item matches exactly one item in every other category, an O lets you put X's in the rest of its row and column, and a row with only one blank cell left must have its O in that blank cell.

Do you ever have to guess in a logic puzzle?

No. A well-made logic puzzle has exactly one solution that can be reached by reasoning alone. What you can do is test a supposition: assume a cell is true, follow the consequences, and if they lead to a contradiction, you've proven the cell is false. That's a valid deduction, not a guess. If the chain doesn't lead to a contradiction, erase everything from the test, because nothing in it has been proven. Using a different pencil color for suppositions makes this cleanup easy.

What is transitivity in a logic puzzle?

Transitivity means carrying facts from one part of the grid to another. If Cara did the sudoku, and the sudoku took 10 minutes, then Cara took 10 minutes. It also works with X's: if Cara did the sudoku, and the sudoku did not take 25 minutes, then Cara did not take 25 minutes. Every time you place an O, look at the other small tables and copy over everything you know about either of the two linked items. Missing this step is the most common reason solvers get stuck.

How do you handle either-or clues?

Read the exact wording first. "Either A or B, but not both" means exactly one is true, so once you prove one part, the other is false, and if you rule out one part, the other must be true. If a clue says only "either A or B" without "but not both," check the puzzle's instructions, because conventions vary. Either-or clues about two descriptions, such as "either the maze solver or the person who took 10 minutes is Ana," often also tell you those two descriptions belong to different people.

What is Einstein's riddle?

Einstein's riddle is a popular name for the zebra puzzle, a logic puzzle about five houses in a row, each with a different color, nationality, pet, drink and cigarette brand. The usual version appeared in Life International in 1962, and there's no evidence Einstein wrote it. Its clues never mention water or the zebra, yet you can deduce who drinks water and who owns the zebra. In the standard version, the Norwegian in the first house drinks water and the Japanese resident in the green fifth house owns the zebra.

How long does it take to solve a logic puzzle?

It depends on the size and the clue types. A three-by-three puzzle with direct clues may take a beginner five minutes, while a four-category puzzle with five items in each, full of comparison and either-or clues, can take an hour. The zebra puzzle is famous partly because it takes most people quite a while on their first try. Speed comes from habits more than talent: clearing rows after every O, carrying facts between tables and re-reading clues after each breakthrough.

Are logic puzzles good for kids?

They can be a great fit, as long as you start small. A three-by-three grid with direct clues lets younger solvers learn the X-and-O system without frustration. Comparison clues and either-or clues can be added once that feels easy. Working in pairs helps, because explaining each mark out loud builds careful reasoning and catches mistakes. Logic puzzles also reward checking your work at the end, which is a good habit in math and reading. Keep the stories playful and the categories familiar, like snacks, pets or favorite colors.

What if a logic puzzle seems to have two answers or none?

If two different answers both fit every clue, re-read the clues for a detail you missed, such as a comparison that rules out ties or an either-or clue that says "but not both." Published puzzles are designed to have exactly one solution, so a second answer usually means a misread clue. If no answer seems to fit, look for an unproven mark you treated as a fact. Erase back to your last certain step and redo the deductions. Homemade puzzles are different: they really can have two answers, which is why puzzle writers test every puzzle before sharing it.

Should I solve logic puzzles in pen or pencil?

Pencil, at least while you're learning. Even careful solvers sometimes place a mark too early, and being able to erase cleanly keeps the grid readable. Many people use two colors: one for proven marks and a second for a supposition they're testing, so they can wipe out a failed test without touching the facts. If you prefer pen, write X's and O's small and keep a separate scrap of paper for what-if chains. Whatever you use, mark only what you've proven, and the grid will stay trustworthy from start to finish.

Sources

We checked every source below while writing this guide. Last reviewed October 30, 2026, by Joan Ramos.

1. Deductive and Inductive Arguments (Timothy Shanahan) (Internet Encyclopedia of Philosophy)
2. Logical Consequence (Jc Beall, Greg Restall and Gil Sagi) (Stanford Encyclopedia of Philosophy)
3. Who Owns the Zebra? (Florida State University, Department of Scientific Computing)
4. CS486/686 Lecture 4: Constraint Satisfaction (Pascal Poupart) (University of Waterloo)
5. The Game of Logic by Lewis Carroll (Project Gutenberg)