Problem of the Week
Problem A and Solution
Track and Field

Problem

Andre, Bilal, Glenna, and Juanita are all friends. They have given each other nicknames as well. The four nicknames are Boss, Buzz, Cosmo, and Tiger. The friends are competing in the track and field day at their school. Using the following clues, determine the nickname of each of the friends.

Clues:

1. Juanita beat Tiger in the \(400\) m race, but Juanita lost to Buzz in the high jump.

2. Glenna and Tiger tied in the long jump, but Boss beat Glenna in the \(1500\) m race.

3. Cosmo, Tiger and Andre found the water station together after the first event.

4. Cosmo and Juanita ran separate legs on the relay race.

The table below, with a column for each name and a row for each nickname, may be helpful in solving this problem.

Solution

We will give the final answer and then show the solution. Andre’s nickname is Buzz, Bilal’s nickname is Tiger, Glenna’s nickname is Cosmo, and Juanita’s nickname is Boss.

Now, each clue eliminates at least one possible person/nickname pair. If Person A is doing something with Person B, then Person A and Person B must be different people. We can put an  in the table where we know someone does not match a nickname.

There are several ways to determine the correct nicknames; here is one way. We can start with the first clue: Juanita beat Tiger in the 400 m race, but Juanita lost to Buzz in the high jump.

Using this information, we can update the table by adding two s in the column for Juanita: an  in the cell for Buzz and an  in the cell for Tiger.

From the second, third, and fourth clues, we can add five new s to the table as follows.

At this point, we know that Juanita must have the nickname Boss, since this is the only nickname left in her column. We can put a check in that box, and eliminate Boss as the possible nickname for everyone else, by putting an  in the remaining empty cells in the row for Boss.

Now we can conclude that Andre must have the nickname Buzz, since this is the only nickname left in his column. We can put a check in that box, and eliminate Buzz as the possible nickname for everyone else.

Next we can conclude that Glenna must have the nickname Cosmo, since this is the only nickname left in her column. We can put a check in that box, and eliminate Cosmo as the possible nickname for Bilal, who is the only person left. The only nickname left is Tiger. That must be Bilal’s nickname. The final version of the table is below.

So Andre’s nickname is Buzz, Bilal’s nickname is Tiger, Glenna’s nickname is Cosmo, and Juanita’s nickname is Boss.