How to Solve Logic Puzzles

To solve a logic puzzle, write down every option, then use each clue to rule options out until only one possibility is left for each item. Start with the clues that give a definite fact, record what you learn in a grid or a list, and go back over the clues each time something new is fixed. When you get stuck, assume one possibility is true and follow it through: if it leads to a contradiction, it must be false.

Logic puzzles train the same habits that logical reasoning tests reward, so they make excellent practice. Once the method feels natural, try it under time pressure in a free logical reasoning test.

The method in five steps

1. List what you are matching. Identify the categories, such as people, projects and floors, and every option in each.
2. Set up a grid or a list. For matching puzzles, draw a grid with one category across the top and another down the side. For ordering puzzles, draw a row of numbered positions.
3. Apply the definite clues first. “Ben works on floor 1” fixes something immediately. Record it, and cross out everything it rules out.
4. Use the conditional clues next. Clues like “the Budget lead works on floor 3” or “T arrives after R” link two facts. Combine them with what you already know.
5. Keep cycling through the clues. Each new fact can unlock a clue that seemed useless before. When every category has exactly one option left, check the solution against every clue.

The two ideas that solve most puzzles are elimination, where an option is ruled out because a clue forbids it, and the “only one left” rule, where an option must be correct because everything else in its row or column has been ruled out.

Worked example 1: a matching grid

Three colleagues, Asha, Ben and Cara, each lead a different project (Audit, Budget or Compliance) and each work on a different floor (1, 2 or 3).

1. Ben works on floor 1.
2. The Budget lead works on floor 3.
3. Cara does not lead Budget.
4. The Compliance lead works on the floor directly above the Audit lead.

Step 1. Clue 1 is definite: Ben is on floor 1.

Step 2. Clue 2 says the Budget lead is on floor 3. Ben is on floor 1, so Ben does not lead Budget.

Step 3. Clue 3 says Cara does not lead Budget either. Only Asha is left, so Asha leads Budget and works on floor 3.

Step 4. Floors 1 and 3 are taken, so Cara is on floor 2.

Step 5. Clue 4 says Compliance is directly above Audit. Ben (floor 1) and Cara (floor 2) lead those two projects, so Audit must be on floor 1 and Compliance on floor 2.

Answer. Asha leads Budget on floor 3. Ben leads Audit on floor 1. Cara leads Compliance on floor 2. Check every clue against this solution: all four hold.

Notice that clue 4 was useless at the start. It only became decisive once the floors were fixed. That is why cycling back through the clues matters.

Worked example 2: putting things in order

Five deliveries, P, Q, R, S and T, arrive one after another.

1. S arrives third.
2. P arrives immediately before S.
3. T arrives after R.
4. Q does not arrive first.
5. T does not arrive last.

Draw five positions: 1 2 3 4 5.

Step 1. Clue 1 puts S in position 3. Clue 2 then puts P in position 2.

Step 2. Positions 1, 4 and 5 are left for Q, R and T. Clue 4 rules Q out of position 1. Clue 3 says T comes after R, so T cannot be first either. That leaves R in position 1.

Step 3. Q and T share positions 4 and 5. Clue 5 says T is not last, so T is fourth and Q is fifth.

Answer. R, P, S, T, Q.

Worked example 3: testing an assumption

Some puzzles give you nothing definite to start with. Then you assume one possibility and see where it leads.

Two people, A and B, each either always tell the truth or always lie. A says: “We are both liars.” What is each of them?

Assume A tells the truth. Then the statement is true, so A is a liar. That contradicts the assumption, so A cannot be a truth-teller.

So A is a liar. That means the statement “we are both liars” is false. A is a liar, so for the statement to be false, B must be a truth-teller.

Answer. A is a liar and B tells the truth.

The skill here is following an assumption all the way to a contradiction. It is the same reasoning you use in a test when you check whether an answer option could possibly be right.

Common mistakes

• Reading a clue backwards. “T arrives after R” does not mean R arrives after T. Restate each clue in your own words before you use it.
• Assuming more than a clue says. “P arrives before S” does not mean immediately before, unless the clue says so.
• Not writing things down. Holding several facts in your head is where errors creep in. A quick grid is faster than starting again.
• Forgetting to recheck clues. A clue that told you nothing at the start may solve the puzzle later.
• Stopping without a final check. Test your answer against every clue. If one fails, find where you went wrong rather than forcing it.

How logic puzzles help with logical reasoning tests

Logic puzzles build exactly the habits that employers’ tests reward: taking conditions literally, recording what you know, eliminating options, and checking the answer against every rule. Rules-based questions in a logical reasoning test are, in effect, short logic puzzles with a time limit.

For more on the skill itself, read what logical reasoning is. For other question types worked through step by step, see our logical reasoning examples with answers. Then put the method to work in a timed logical reasoning practice test.