Favorite Fruit and Favorite Color

Ava, Beth, Cam, and Derek each have a different favorite fruit and favorite color. We know their favorite fruits are apple, banana, cherry, and durian, and their favorite colors are blue, green, red, and yellow. We also know:

  1. Cam does not like apples or cherries
  2. Derek’s favorite color is yellow and his favorite fruit is not banana
  3. The person whose favorite fruit is cherry also likes the color green
  4. Beth’s favorite color is red and her favorite fruit is not apple
  5. The person whose favorite fruit is durian does not like the color blue

What is each person’s favorite fruit and favorite color?


Solution

  • Ava: cherry, green
  • Beth: durian, red
  • Cam: banana, blue
  • Derek: apple, yellow

The easiest way to solve this is to draw a grid with each person in the rows and each color and fruit in the columns, marking which colors and fruits they like or don’t like.

After filling in the information from statements #1, 2, and 4, we see that statement #3 can only refer to one person, Ava, because Beth and Derek’s favorite colors are already known and Cam does not like cherries.

Then Cam’s favorite color must be the last remaining color, blue.

Then we see Beth and Cam’s favorite fruits can only be banana and durian, so Derek’s favorite fruit must be apple.

Finally, statement #5 shows us Cam could not have durian as a favorite fruit, so Beth’s favorite fruit must be durian and Cam’s must be banana.

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