In a group of 25, you might have good odds of duplicate birthdays, as the linked question says, but you have almost good odds of not having them, too. For all ten groups of 25 to have duplicates is unlikely.
But this is not a group of 250 random people. It's an exam, and since it's teenagers, it is perhaps a high-school exam -- a situation in which people ...
Here's a solution using only language structure:
CHILE, BELIZE, INDIGO - Contains the letter I
CHILE, RAZOR, BLUNT - Has 5 Letters
CHILE, BABAHOYO, HAZELNUT - Contains the letter H
BELIZE, BABAHOYO, BLUNT - Contains the letter B (Starts with it even)
BELIZE, HAZELNUT, RAZOR - Contains the letter Z
INDIGO, HAZELNUT, BLUNT - Contains the letter N