Solve this birthday riddle with a little logic and math power

It’s a real head-scratcher.

A promotional photo for a Twilight Zone episode called Long Distance Call.
Can you guess the old woman’s birthday? CBS Television

We know you are bored at home right now—we are too. Here are some puzzles and brainteasers to challenge your family and friends with, either in person or over video chat. In this post, try your hand at a calendar riddle.

An old crone blocks your path with a riddle. She demands you guess her birthday. She gives you all a list of 10 possible dates, and separately tells your two friends—Charles and Barbara—the month and day of her birth, respectively. Charles is pretty sure this problem showed up on his Facebook feed in 2015, but he doesn’t recall how to solve it.

The 10 possible dates the old woman gives you, Barbara, and Charles are listed below, in chronological order.

  • May 15, May 16, May 19
  • June 17, June 18
  • July 14, July 16
  • August 14, August 15, August 17

After scrutinizing the dates, Charles and Barbara respond as follows:

Charles: “I’m not sure when her birthday is, but I am sure that Barbara can’t guess.”

Barbara: “I couldn’t guess before, but I can now!”

Charles: “Great! Then I know her birthday too.”

Based on this dialogue, when is the old woman’s birthday?

Correction: The information that Charles and Barbara received from the old woman was switched when this article was first posted online.


Click here to see the answer to the riddle.

This article was originally published in the Winter 2018, Danger issue of Popular Science.




Claire Maldarelli

Claire Maldarelliis the Science Editor at Popular Science. She has a particular interest in brain science, the microbiome, and human physiology. In addition to Popular Science, her work has appeared in The New York Times, Scientific American, and Scholastic’s Science World and Super Science magazines, among others. She has a bachelor’s degree in neurobiology from the University of California, Davis and a master’s in science journalism from New York University's Science, Health, and Environmental Reporting Program. Contact the author here.