Introduction:
I am here, again to make a new math note. Today I start learning math detective tasks. This is another kind of math problems with one solution which will help you every time.

The task:

Three friends — Alex, Ben, and Chloe — each play a different sport (basketball, volleyball, tennis) and each has a different favorite color (blue, green, red).
Use the clues to find each person's sport and favorite color.

### Clues
Alex does not play basketball. 
The volleyball player likes green. 
Ben's favorite color is not blue. 
Chloe does not play tennis. 
The person who likes red plays basketball. Alex likes blue.
Ben does not play volleyball.

This is the task that I will work on.

The solution:
I always solve math detective tasks with a table. So let's make one for this
time:

Here is my table. I see the 3 friends and what I am searching (the sport and the favorite color). Know let's look at the clues and put ticks and hicks, where I need.

### CLUE ONE
Alex does not play basketball.

I put hicks on Alex and basketball because I understood that Alex doesn't play basketball.

### CLUE TWO
The volleyball player likes green.
With this clue I can't write anything , cause I don't know who is the volleyball player or who likes green.

### CLUE THREE
Ben's favorite color is not blue.

Do I need to say why I put it there? I think no, so let's continue

### CLUE FOUR
Chloe does not play tennis.

### CLUE FIVE
The person who likes red plays basketball.
Here I thought I can't write nothing, but… Look close! The person who likes red plays basketball? Do you find it? Comment down below did you. Now I will say it. The person who likes red plays basketball - we know that Alex doesn’t play basketball… so he doesn’t like red.

### CLUE SIX
Alex likes blue.

Here is my first tick. An important thing. When I write a tick I need to put hicks in the column and the line. Maybe you don't understand. I will show you:

I will tell you why. I put the yellow hicks, because when I know that Alex likes blue, that automatically tell us that this isn't Ben or Chloe's favorite color. The reason why I put the orange one is similar - when I know that Alex's favorite color is green I automatically understand that the other colors aren’t his favorites.

And now the last clue.
### CLUE SEVEN
Ben does not play volleyball.

Know I thought I have nothing to do, but look on another way. I had one no used clue. Let's see it:

### CLUE TWO
The volleyball player likes green.

It's a little bit difficult to understand it. The volleyball player likes green. What we know about green? … Alex does not like green. So he isn't the volleyball player:

With that we understand that Alex plays tennis, because he don't play basketball or volleyball and the sport that is left is tennis. We also don't forget to put hicks in the tennis' column and Alex's line.

I look carefully at the table. And I see the column with the volleyball. The only place where we can put tick is the last line. So… let’s put it.

The sport that is left for Ben is basketball so I will put this tick too.

And the last thing is to find whose favorite color is green and who's red.

Now look at clue number five. We know that Ben plays basketball, so his favorite color is red. Also the color left for Chloe is green. Let’s write it in the table.

The answer:
Finally! I found the answer. And the exercise wants to tell it so it is here:

Alex
FAVORITE COLOR:  Blue
SPORT:  Tennis

Ben
FAVORITE COLOR:  Red
SPORT:  Basketball

Chloe
FAVORITE COLOR:  Green
SPORT:   Volleyball

End:
A very long lesson, right? We finally did it. You see that the math detective tasks aren't very difficult. Know enjoy your break. You need it after this long lesson. Bye!