Have you ever kept a secret? A secret is something you know that you aren’t supposed to tell anyone else. You might be the only person who knows, or maybe you heard the story from someone else. There have been some famous secrets in history, like when Alexander Hamilton and others moved the US capital from New York to Washington, DC. Then there’s the formula for Coke, which only 2 people know at any time. The thing is, people aren’t so good at keeping secrets. They say, “Oh, I’ll just tell my one friend and tell her not to tell anyone…” Then that friend might tell 1 friend and say the same thing…If you do the math, pretty soon 15 or 20 people know, even though no one was supposed to talk about it!
Wee ones: If you know a secret that you tell to a friend, and your friend tells a friend, at least how many people know the secret now?
Little kids: If you spill a secret to 2 friends, who each tell 2 friends, at least how many people know the secret now? Bonus: If you hear the secret at 2 pm, tell your friends 2 hours later, and they tell their friends 2 hours after that, at what time do the last people hear it?
Big kids: Let’s say each person tells 3 people a secret. Starting with that first person, how many rounds of telling does it take for at least 30 people to hear it? (To be clear, the first person telling 3 people counts as the 1st “round” — and it’s always new people who hear it.) Bonus: How many new people hear it in the round after that?
Wee ones: 3 people.
Little kids: 7 people: you, your 2 friends, and the 4 people they told. Bonus: At 6 pm.
Big kids: It takes just 3 rounds, the 1st round adds 3 friends, then they add 9 (for a total of 12 + the starter), then those 9 people add 27 more (for a total of 12 + 27 + the starter, or 40 people). Bonus: 81 people (27 x 3).
Now here’s a JUICY SECRET: how many people have the same exact birthday as you? Find out tomorrow on Bedtime Math!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.