Techniques for Solving Logic Puzzles. Logic Puzzles Logic puzzles operate using deductive logic....

Techniques for Solving Logic Puzzles

Logic PuzzlesLogic puzzles operate using

deductive logic.A well-designed logic puzzle has

only one correct answer, and one can use the available information to discover that answer.

There are an unlimited number of types of logic puzzles, and no set of guidelines can cover all of them. You must use your own ingenuity to modify these guidelines to fit new situations.

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Logic Puzzles

Basic steps to solving logic puzzles

1. Read the prompt carefully. What will a solution include?

2. Devise a method for capturing and displaying all of the possible solutions.

3. Use the information given and deductive logic to rule out solutions. (Use reductio if needed)

4. Only one solution should remain, and it must be the correct solution. You’re done!

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Logic Puzzles

Let’s apply these steps to an actual logic puzzle.

You are trying to find out which of your three friends are going to the prom. Use the information below to determine which friends are going and which are not.

1. At least one of your friends is going.2. If Susan is going, then Tammy isn’t.3. Either Susan is going, or Ursula isn’t.4. If only one person went, it was not Susan.5. If Tammy did not go, then neither did Ursula.

This is a fairly standard logic puzzle. With a little ingenuity, we should be able to figure it out.

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Logic Puzzles

Let’s apply these steps to an actual logic puzzle.



This is a fairly standard logic puzzle. With a little ingenuity, we should be able to figure it out.

Step One: Read Carefully. Determine the solution requirements

There seems to be only one dimension called for in the solution. For each of your friends, either she is going or she isn’t. You are done once you determine which friends are going and which ones are not.

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Step two: devise a method to display all possible solutions

First, we should consider just listing each person with a box for yes or no. Let’s see what that would look like.

Susan

Tammy

Ursula

Our convention will be to put an “X” in a box when it is proven false, and a check when proven true. An open box means we have not yet determined anything.

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For example, given the chart above, it would indicate that Susan and Ursula are going, and Tammy is not.

Susan

Tammy

Ursula

Let’s go through each statement and see if it would allow us to rule in or out any of our boxes.

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Statement one simply indicates that there will be at least one box which has a check.

Susan

Tammy

Ursula

Unfortunately, it doesn’t tell us how many, or which ones. In fact, it doesn’t allow us to put an “X” or a check anywhere. Let’s move on.

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Statement two tells us that if there is a check next to Susan, then there is an “X” next to Tammy.

Susan

Tammy

Ursula

Since we don’t know if there is a check next to Susan, it really doesn’t allow me to do anything. Remember, these are conditional statements.

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Statement three guarantees that either there is a check next to Susan, or an “X” next to Ursula.

Susan

Tammy

Ursula

Unfortunately, either possibility is still open, and the statement doesn’t allow us to fill in anything.

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Statement four let’s us know that if only one person went, it had to be Tammy or Ursula.

Susan

Tammy

Ursula

But we don’t even know if it was only one person, so that really doesn’t help us.

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Statement five indicates that if there is an “X” next to Tammy, then there is an “X” next to Ursula.

Susan

Tammy

Ursula

By itself, this statement does not allow us to mark our grid. We don’t know if there is an “X” next to Tammy.If you have already begun thinking hard, you can use hypothetical reasoning (reductio ad absurdum) to solve this puzzle as it stands using this grid. If so, you are very smart! What do you need me for?

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Perhaps we should try to rethink our possible solutions, and display them in a new way.

Susan

Tammy

Ursula

If we think about it, we can make a list of all the possible combinations we might find in our solution. Think hard on your own to see if you can list them.

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There are eight possibilities, so we need some more room. Let’s move things around.

Susan

Tammy

Ursula

Using the statements below, determine which of your friends is going to prom.

1. At least one of your friends is going.

2. If Susan is going, then Tammy isn’t.

3. Either Susan is going, or Ursula isn’t.

4. If only one person went, it was not Susan.

5. If Tammy did not go, then neither did Ursula.


Did you get all eight possibilities?Using our new grid, let’s see if we can use the available information to rule out any possible solutions.

1. Susan, Tammy, and Ursula

2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

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Step three: using deductive logic to eliminate solutions

Statement one allows us to rule out the eighth solution, so let’s mark it with an “X”.


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

The circled 1 let’s us know what statement we used to rule out this solution. It allows us to check our answers or backtrack when we get stuck.

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Think about statement two. It says that if Susan is one of the members of our solution, then Tammy is not.


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

That allows us to rule out any solution which includes Susan and Tammy, solutions one and two. Let’s mark those.

Click to proceed








Statement three is a little tougher. It allows us to rule out any solution which does not include Susan, but


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

does include Ursula. In solution 5 and 7, Susan is not going, but Ursula is, which would make statement 3 false.

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2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

That means we can rule out solutions 5 and 7, and we can cross them off our list.

Click to proceed








Statement four allows us to rule out solution 4.


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

Now, there are only two possible solutions left, and one more statement we can use. Hopefully, it allows us to rule out one solution. Click to proceed








Statement five indicates that if Tammy is not a part of our solution, then neither is Ursula. In solution 3, Tammy is not present, but Ursula is. So statement five allows us to rule it out.


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

Click to proceed







Step four: the only remaining solution must be correct

Since the sixth solution is the only one which remains after applying all of our information, it must be the correct solution.


2. Susan and Tammy

3. Susan and Ursula

4. Susan

5. Tammy and Ursula

6. Tammy

7. Ursula

8. None

So, Tammy is going to prom, and Susan and Ursula are not. We’re done!

Click to proceed

Logic PuzzlesRemember, not every logic puzzle will be solved in the same way as this one. You need to use your creativity in devising solution

grids and other techniques

Keep in mind that one kind of grid can make a solution more or less

difficult than another.

Check back for presentations on hypothetical reasoning and multi-dimensional solutions.

Wasn’t that fun!

Techniques for Solving Logic Puzzles. Logic Puzzles Logic puzzles operate using deductive logic....

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