Techniques for Solving Logic Puzzles

1. Techniques for Solving Logic Puzzles

2. Logic Puzzles • Logic 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. Click to proceed

3. Logic Puzzles Basic steps to solving logic puzzles • Read the prompt carefully. What will a solution include? • Devise a method for capturing and displaying all of the possible solutions. • Use the information given and deductive logic to rule out solutions. (Use reductio if needed) • Only one solution should remain, and it must be the correct solution. You’re done! Click to proceed

4. 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • 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. Click to proceed

5. Step One: Read Carefully. Determine the solution requirements 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. 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. This is a fairly standard logic puzzle. With a little ingenuity, we should be able to figure it out. Click to proceed

6. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. First, we should consider just listing each person with a box for yes or no. Let’s see what that would look like. 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. Click to proceed

7. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.    For example, given the chart above, it would indicate that Susan and Ursula are going, and Tammy is not. Let’s go through each statement and see if it would allow us to rule in or out any of our boxes. Click to proceed

8. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Statement one simply indicates that there will be at least one box which has a check. 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. Click to proceed

9. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Statement two tells us that if there is a check next to Susan, then there is an “X” next to Tammy. 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. Click to proceed

10. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Statement three guarantees that either there is a check next to Susan, or an “X” next to Ursula. Unfortunately, either possibility is still open, and the statement doesn’t allow us to fill in anything. Click to proceed

11. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Statement four let’s us know that if only one person went, it had to be Tammy or Ursula. But we don’t even know if it was only one person, so that really doesn’t help us. Click to proceed

12. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Statement five indicates that if there is an “X” next to Tammy, then there is an “X” next to 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? Click to proceed

13. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. Perhaps we should try to rethink our possible solutions, and display them in a new way. 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. Click to proceed

14. Step two: devise a method to display all possible solutions • 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. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula. There are eight possibilities, so we need some more room. Let’s move things around.

15. Step two: devise a method to display all possible solutions • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • 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. Click to proceed

16. Step three: using deductive logic to eliminate solutions • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.  Statement one allows us to rule out the eighth solution, so let’s mark it with an “X”. 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. Click to proceed

17. Step three: using deductive logic to eliminate solutions  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.   Think about statement two. It says that if Susan is one of the members of our solution, then Tammy is not. That allows us to rule out any solution which includes Susan and Tammy, solutions one and two. Let’s mark those. Click to proceed

18. Step three: using deductive logic to eliminate solutions  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.   Statement three is a little tougher. It allows us to rule out any solution which does not include Susan, but does include Ursula. In solution 5 and 7, Susan is not going, but Ursula is, which would make statement 3 false. Click to proceed

19. Step three: using deductive logic to eliminate solutions  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.     That means we can rule out solutions 5 and 7, and we can cross them off our list. Click to proceed

20. Step three: using deductive logic to eliminate solutions  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.      Statement four allows us to rule out solution 4. 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

21. Step three: using deductive logic to eliminate solutions  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.       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. Click to proceed

22. Step four: the only remaining solution must be correct  • Using the statements below, determine which of your friends is going to prom. • At least one of your friends is going. • If Susan is going, then Tammy isn’t. • Either Susan is going, or Ursula isn’t. • If only one person went, it was not Susan. • If Tammy did not go, then neither did Ursula.        Since the sixth solution is the only one which remains after applying all of our information, it must be the correct solution. So, Tammy is going to prom, and Susan and Ursula are not. We’re done! Click to proceed

23. Logic Puzzles Remember, 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!