GeekDad Puzzle of the Week – Friend Diagrams

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Looking through my list of friends recently on my favorite social media platform, I noticed that people tended to fall into a small number of “sets.” That is, if you I knew you through work, I probably did not grow up with you, and if you fell into one of these two groups, I probably didn’t go to college with you.

However, looking at the characteristics of people’s first names, it was easy to construct multiple criteria that multiple had in common. For example, both “David” and “Penny” have not only 5 letters in their names, but also have a repeated letter, where “Debra” and “Adam” meet one or the other criteria, but not both, and “Mike” meets neither.

friendDiagramEach given criteria can split your list of friends into two groups: those that meet the criteria, and those that don’t. Given four criteria, you can split a list of people into some 16 groups.

Below is a list of 4 criteria, and 47 different names. The four criteria individually each split the group exactly in half, and, when applied together, split the list into equal groups — almost.

This week’s Geekdad Puzzle of the Week: Which of the 16 groups defined by these 4 criteria only has two members (and not three like the rest)?

Criteria #1: An odd number of letters in their name.
Criteria #2: Their name sums to a prime (A=1, B=2,.. Z=26, so ADAM=19, etc.)
Criteria #3: Duplicates a letter (like DAVID or SCOTT.)
Criteria #4: Has an even number of vowels (A,E,I,O, and U only.)

List of names:

ADAM
ALLISON
AMBER
ANGELA
ASTRID
BETSY
BRITTANY
CANDACE
CARMELO
CATHERINE
CHIQUITA
CHRISTIAN
CLAUDIA
DAMON
DAVID
DWIGHT
ELEANOR
HENRY
HUNTER
JACKSON
JACQUELINE
JULIET
KATE
LAUREN
LILY
LOUISA
MANDI
MATT
MAX
MICHELLE
MILLICENT
NORA
OCTAVIA
PENNY
PORTIA
RILEY
ROBERT
SABINE
SCARLETT
SCOTT
SHAWN
TOBIAS
TODD
VICTORIA
WANDA
WENDY
WILFRED

Given the list above, ADAM is one of the three names that fails Criteria #1, but meets #2, #3, and #4.

As always, please send your response into GeekDad Central. The winner of this week’s fabulous prize, a $50 Gift Certificate from our friends at ThinkGeek, will be determined by a random drawing from among the correct (or at least reasonably well-reasoned) entries.

Good luck, and happy puzzling!

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