Math and Logic

Can You Solve by Eliminating?

Information is much easier to interpret when it's organized well. For example, consider the statements below:

There are three tables in a line. They each have a different number of people and a different dish being served.

  1. The soup is right of the table with two guests.
  2. Three people are at the table with sandwiches.
  3. The leftmost table has salad.
  4. The middle table has one guest.

This is a bit of a mess.

Sometimes in life — and often in logic puzzles — information is presented in this disorganized way, and a large part of the problem is just organizing the information in order to make it understandable.

One way to do this is with a grid like the one below. It shows the relationships between objects in the problem.

The goal is to record the information in this grid in order to make connections clearer. Let's look at how the first piece of information can be recorded. Since statement 1 tells us the soup is right of the table with two guests, we can conclude the following:

  • The soup is not at the left-hand table.
  • The table with two guests is not the right-hand table.
  • The table with two guests does not have soup.

All of these are recorded here:

Let's fill in the grid with the rest of the information provided:

Once we've done this, many things become clearer — for example, the right-hand table must have three guests. This is certainly to be true because we know that the middle table has one guest and we also know (from the first statement) that the table with two guests cannot be on the right. The only table that could have three guests then is the right-hand table. Working from here, we can piece together the rest of the puzzle pretty quickly.

Today's Challenge

There are four people living in four differently colored houses, and every one of them has a different pet.

The houses aren't necessarily in this order. The houses aren't necessarily in this order.

  1. Annie does not live in the red house.
  2. The fish lives in the orange house, which is not Annie's.
  3. Becca owns the lizard and does not live in the yellow house.
  4. Dante's house is red.
  5. The hamster lives in the yellow house.

Which person has a hamster?