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Solving Word Problems with a Logic Grid Many word problems ask you to relate two sets of data. For example, one set of data might be people, and the other set might be their favorite season. You might be asked to figure out the favorite season of four people by analyzing several clues. To solve this type of problem we can use a logic grid. A Logic Grid looks like this:
Let’s say that you are told that four people in your class, Betsy, Paul, Melvin and Anne each have a favorite season. You are also told that they all like different seasons. You are asked, what is Betsy’s favorite season Then you are given these hints: Melvin likes to go to the beach. Betsy does not like snow. Paul does not like spring flowers. Anne likes to go skiing. We first set up our Logic Grid like this:
First, we know that Melvin likes to go to the beach, so let’s put an F for favorite in Melvin’s row under the Summer column. Since Melvin is the only one who likes Summer, we can put X’s in the other rows (X means not the favorite). We can also put X’s in Melvin’s row for the other seasons.
Next, we know that Betsy does not like snow. Let’s put an X in Betsy’s row under the Winter column.
Next, we know that Paul does not like spring flowers. He probably is allergic to them and sneezes a lot during the Spring. Let’s put an X in Paul’s row in the Spring column.
Now we know that Anne likes to go skiing. In Anne’s row we can put an F Winter column, and X’s in the other columns. We can also put X’s in the other columns in Anne’s row.
Now we notice that Paul does not like Winter, Spring or Summer. He must like Fall, the only season left. Let’s put an F in Paul’s row under Fall, and X’s in the other rows under Fall
Finally, we notice that Betsy does not like Winter, Summer or Fall. She must like Spring. We can put an F in Betsy’s column under Spring.
Betsy’s favorite season is Spring. She doesn’t have allergies. More fun – Now try to solve the same problem with one change. Some of the students may like the same season, but each season is liked by at least one student. Here are the same hints: Melvin likes to go to the beach. Betsy does not like snow. Paul does not like spring flowers. Anne likes to go skiing. We start again with the same logic diagram:
Since Melvin likes to go to the beach, let’s put an F in his row under Summer. And we can put X’s in his row under the other seasons. But since one of the other students may also like Summer, we can’t put X’s in the other rows under Summer.
Now, since Betsy does not like snow, we can put an X in her row under Winter.
And since Paul does not like Spring flowers, we can put an X in his row under Spring.
Anne likes to go skiing, so we can put an F in her row under Winter, and X’s in her row under the other seasons.
Now we notice that Spring is not liked by 3 of the 4 students, but we know that each season in liked by at least one student. So it must be Betsy. Let’s put an F in Betsy’s row under Spring, and X’s in Betsy’s row under the other seasons.
Now we are left with Paul. Paul’s favorite season could be Winter, Summer or Fall. Since we were told that each season was liked by at least one student, we must pick Fall. Here is the final diagram:
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