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Techniques for Solving Logic Puzzles

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Logic Puzzles Logic puzzles operate using deductive logic. 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. 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. 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

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Logic Puzzles Basic steps to solving logic puzzles Read the prompt carefully. What will a solution include? Read the prompt carefully. What will a solution include? Devise a method for capturing and displaying all of the possible solutions. 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) 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. Youre done! Only one solution should remain, and it must be the correct solution. Youre done! Click to proceed

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Logic Puzzles Lets 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 isnt. 3.Either Susan is going, or Ursula isnt. 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. Click to proceed

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Logic Puzzles Lets 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 isnt. 3.Either Susan is going, or Ursula isnt. 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. 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 isnt. You are done once you determine which friends are going and which ones are not. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. 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. Lets 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. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions For example, given the chart above, it would indicate that Susan and Ursula are going, and Tammy is not. Susan Tammy Ursula Lets go through each statement and see if it would allow us to rule in or out any of our boxes. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions Statement one simply indicates that there will be at least one box which has a check. Susan Tammy Ursula Unfortunately, it doesnt tell us how many, or which ones. In fact, it doesnt allow us to put an X or a check anywhere. Lets move on. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions 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 dont know if there is a check next to Susan, it really doesnt allow me to do anything. Remember, these are conditional statements. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions 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 doesnt allow us to fill in anything. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions Statement four lets us know that if only one person went, it had to be Tammy or Ursula. Susan Tammy Ursula But we dont even know if it was only one person, so that really doesnt help us. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions 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 dont 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

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions 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. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions There are eight possibilities, so we need some more room. Lets move things around. Susan Tammy Ursula

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step two: devise a method to display all possible solutions Did you get all eight possibilities? Using our new grid, lets 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 Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate solutions Statement one allows us to rule out the eighth solution, so lets mark it with an X. 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 The circled 1 lets 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

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate solutions Think about statement two. It says that if Susan is one of the members of our solution, then Tammy is not. 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 That allows us to rule out any solution which includes Susan and Tammy, solutions one and two. Lets mark those. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate solutions Statement three is a little tougher. It allows us to rule out any solution which does not include Susan, but 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 does include Ursula. In solution 5 and 7, Susan is not going, but Ursula is, which would make statement 3 false. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate 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 That means we can rule out solutions 5 and 7, and we can cross them off our list. Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate solutions Statement four allows us to rule out solution Susan, Tammy, and Ursula 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

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. Step three: using deductive logic to eliminate solutions 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. 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 Click to proceed

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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 isnt. 3.Either Susan is going, or Ursula isnt. 4.If only one person went, it was not Susan. 5.If Tammy did not go, then neither did Ursula. 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. 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 So, Tammy is going to prom, and Susan and Ursula are not. Were done! Click to proceed

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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. Wasnt that fun!

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