How to Solve a Logic Grid Puzzle: A Step-by-Step Guide

To solve a logic grid puzzle, draw a grid that pairs every item in one category with every item in the others, then use each clue to mark a pair as impossible (×) or confirmed (●). Because every item matches exactly one item in each other category, each confirmed pair rules out others, and the marks keep spreading until only one arrangement is left.

You do not need to guess, and you do not need any maths. The skill is bookkeeping: writing down each fact the moment it becomes certain, then re-reading the clues with the new facts in mind. This guide explains the idea, shows how to set the grid up, gives a method you can follow on any puzzle, and walks through one complete example, mark by mark.

What is a logic grid puzzle?

A logic grid puzzle is a short story plus a list of clues. The story names a few categories of things, such as three neighbours, three treats and three arrival times. Your job is to work out which item in each category goes with which item in the others.

Three rules hold in nearly every puzzle:

• One-to-one matching. Each person has exactly one treat and exactly one arrival time, and no two people share one.
• The clues are all you have. Everything you need is stated or follows from what is stated. If the puzzle does not say it, do not assume it.
• The grid is only a notebook. It does not solve anything. It stops you from forgetting a fact you have already worked out.

Clues come in a few shapes. A negative clue tells you two things do not go together ("Theo did not bring the pie"). A positive clue tells you they do ("The cookies arrived at 9:00"). An ordering clue compares positions ("Maya arrived later than Theo"). Longer puzzles add more shapes, which come up below.

How do you set up the grid?

Draw one table that lists every pair of categories you might need to match. With three categories, the usual layout is an "L": the first category runs down the left side, the second runs across the top, and the third is added so that every category meets every other one exactly once.

For the bake sale example later in this guide, the blank grid looks like this. Each cell answers one question, such as "Did Maya bring the cake?" or "Did the pie arrive at 10:00?"

Use two marks, and keep them the same for the whole puzzle:

Mark	Meaning
×	These two cannot go together.
●	These two go together.

Some solvers prefer ✓ and ✗, or a dot and a dash. Any pair works. What matters is that a blank cell means "not known yet", never "probably not". A grid with honest blanks tells you exactly where to look next.

Pencil is better than pen, and a clue list you can tick off helps. Neither is required.

What is the step-by-step method?

The same short routine works on small puzzles and large ones.

1. Read the question first. The last sentence says what you must find. It also tells you when you are finished.
2. List the categories and the items in each. Check the grid has a row or column for every one.
3. Mark the direct negative clues. "Theo did not bring the pie" is one × in one cell.
4. Mark the direct positive clues. "The cookies arrived at 9:00" is one ●.
5. Apply one-to-one elimination. When a pair is ●, every other cell in that row and column of that block becomes ×. When a row has only one cell left that is not ×, that cell becomes ●.
6. Combine clues. Two partly useful clues often settle something together that neither settles alone.
7. Re-read the grid after every confirmed fact. A new ● usually unlocks several more marks, including in other blocks.
8. Handle ordering clues carefully. Work out what the clue rules out, not only what it rules in.
9. Test a conditional clue only if you must. More on this below.
10. Check the finished grid against every clue. One slip, and this catches it.

Each step exists for a reason. Starting with the question stops you solving the wrong thing. Marking direct clues first gives you facts that cost nothing. Elimination is the engine: it is why a puzzle with only a handful of clues can still have exactly one answer. And the final check is what separates a solution from a lucky arrangement that happens to look right.

A worked example, from blank grid to answer

Here is a small original puzzle. It is not taken from any book.

It has five clues, and every one is needed: remove any one of them and a second arrangement fits. We will use them in a sensible order rather than the order they are printed, because solving rarely follows the printed order.

Step 1: Mark what the clues say outright

Four clues can go straight onto the grid. Clues 1, 4 and 5 each give a ×: Theo and the pie, Zoe and the cake, and the cake and 10:00 do not go together. Clue 2 gives a ●: the cookies arrived at 9:00. Clue 3 has to wait, because it compares two people rather than naming a pair.

Step 2: Use one-to-one elimination on the treats and times

Each treat arrived at exactly one time, and each time has exactly one treat. The cookies took 9:00, so the pie and the cake cannot also have 9:00, and the cookies cannot have 10:00 or 11:00.

Now look at the cake. It is ruled out at 9:00 by the cookies, and at 10:00 by clue 5. Only 11:00 is left, so the cake arrived at 11:00. The pie can then have neither 9:00 nor 11:00, so it arrived at 10:00. We have not learned who brought what yet, but the treat-and-time block is finished.

Step 3: Use the ordering clue

Clue 3 says Maya arrived later than Theo. That rules out two things. Maya cannot be the first to arrive, so she is not at 9:00. Theo cannot be the last, so he is not at 11:00. Notice that the clue does not say Maya is at 11:00 or that Theo is at 9:00. Only the two impossible positions can be marked.

Step 4: Combine two blocks to settle Theo

Now read across the blocks, because the treat-and-time block links the other two. Whoever arrived at 9:00 brought the cookies, and Maya is not at 9:00, so Maya did not bring the cookies. Whoever arrived at 11:00 brought the cake, and Theo is not at 11:00, so Theo did not bring the cake. Clue 1 already ruled out the pie for Theo. That leaves the cookies, so Theo brought the cookies, which means he arrived at 9:00.

With Theo's row complete, 9:00 and the cookies are taken, so Zoe is not at 9:00 and did not bring the cookies.

Step 5: Finish with what is left

Zoe cannot have the cake (clue 4) or the cookies, so she brought the pie, which arrived at 10:00. Maya is left with the cake and 11:00.

The answer: Theo brought the cookies at 9:00, Zoe brought the pie at 10:00, and Maya brought the cake at 11:00.

Now do the last step of the method and check it against every clue. Theo did not bring the pie: correct, he brought cookies. The cookies arrived at 9:00: correct. Maya (11:00) arrived later than Theo (9:00): correct. Zoe did not bring the cake: correct, she brought the pie. The cake (Maya's) did not arrive at 10:00: correct, it arrived at 11:00. All five clues hold.

Which strategies do you actually need?

Not every puzzle needs every technique. In rough order of how often you will reach for them:

Direct deduction. A clue states a fact and you mark it. Almost every puzzle starts here.

Elimination. A ● removes the rest of its row and column in that block; a row down to one open cell gains a ●. This does most of the work in small puzzles.

Cross-referencing. Two blocks share a category, so a fact in one is a fact in the other. In Step 4, "9:00 is the cookies" and "Maya is not at 9:00" together gave "Maya did not bring the cookies". When you are stuck, scan for a ● in one block that has not yet been copied across.

Chained deductions. One new fact enables a second, which enables a third. In the example, the ×s on the cake produced the cake's time, which produced the pie's. Re-reading the grid after each ● is what makes chains visible.

Ordering clues. "Before", "after", "earlier" and "later" usually rule out end positions first, as in Step 3. A clue with a stated gap ("two hours after") rules out more. See the next section for the wording to watch.

Conditional clues. "If Ben ordered tea, then Cara ordered coffee" says nothing until you know whether Ben ordered tea. It also works backwards: if Cara did not order coffee, Ben did not order tea. Leave a conditional clue alone until one half of it is known, then use it.

Contradiction, as a last resort. If nothing else works, you can ask "what if this cell were ●?", follow the consequences, and see whether a clue is broken. If one is, the cell is ×. Do this on scrap paper or in light pencil, and only when the direct methods are exhausted. A guess that happens to survive for a few steps proves nothing.

What mistakes should you avoid?

Most wrong answers come from a few repeating errors:

• Assuming something the puzzle did not say. "Maya arrived later than Theo" does not mean one hour later, or that nobody arrived between them.
• Forgetting one-to-one elimination. After writing a ●, the rest of its row and column must be crossed out. Skipping that step is the most common reason for being stuck.
• Treating a guess as a fact. If you tried something to see what happens, mark it as a trial, or erase it. A trial mark left in ink corrupts every later deduction.
• Not carrying a fact across blocks. A ● in one block usually implies marks in the others. If you stall, look for facts you wrote down but never used elsewhere.
• Misreading ordering words. "Before" is not "immediately before". "Next to" allows either side. "Either A or B" allows one, and it may be both only if the puzzle says so. Read these words slowly.
• Skipping the final check. It takes under a minute. Run each clue against the finished answer, one at a time.

Frequently asked questions

What is the easiest way to start a logic grid puzzle?

Read the question, then mark every clue that names a specific pair, whether positive or negative. Those marks cost nothing and often unlock a chain straight away. Leave clues that compare two things for the second pass.

What does an X mean on a logic grid?

It means the two items cannot go together. A ● (or a ✓) means they must. A blank cell means you do not know yet. Using blank for "no" is the habit most worth breaking.

What do I do when I get stuck?

Look for a ● in one block that is not yet reflected in the others. Then re-read each unused clue with all your current marks in front of you; a clue that looked useless earlier often becomes decisive. If you still cannot move, check for an earlier mistake: two ●s in one row, or a clue that your marks contradict.

Should you guess in a logic grid puzzle?

Not in the sense of picking a cell and hoping. A well-made puzzle can be solved by reasoning alone. A trial with a contradiction can be a fair last resort, as described above, as long as you treat it as an experiment and not as a fact.

Are logic grid puzzles good for beginners?

Yes, if you start small. A three-category, three-item puzzle like the one above has only 36 possible complete arrangements and just five clues. Larger puzzles use the same moves with more rows and more clues.

Can a logic grid puzzle have more than one answer?

Published puzzles are generally designed to have one. If you end up with two arrangements that both fit, reread the clues for a word you skipped, such as "not" or "later", before concluding the puzzle is faulty.

Where to go next

The quickest way to improve is to solve more puzzles, a little harder each time: four items per category, then five, then a puzzle that adds a timeline or a floor plan. If you would like ready-made practice in the form of short detective stories, each with its own grid, The Detective's Logic Casebook has 40 of them in four levels, and our logic and detective puzzle books page compares it with a word-search take on the same idea. Plenty of free puzzle books and websites teach the same method, and the method does not depend on any of them.

In short: draw the grid, mark what is certain, let one-to-one elimination spread the marks, re-read the clues each time something changes, and check the answer against every clue before you stop.