Today’s puzzle was suggested to me by Bobby Seagull, who was told it by his brother, who was told it by a Cambridge don.
Four friends each have a different piece of gossip. They are all in separate locations, and can communicate only via their phones.
1) What is the smallest number of text messages that they need to send between each other to guarantee that everyone knows all the gossip? (In other words, what’s the most efficient texting strategy to make sure each person has every piece of gossip? A text message goes from one person to one person, i.e. if you send one message to two recipients that would count as two messages.)
2) What is the smallest number of phone calls they need to make between each other to guarantee that everyone knows all the gossip? In a phone call between two friends, each person can share what they know with the other.
Let’s enlarge the group now to eight friends. Again, each person is in a separate location and each has a different piece of gossip.
3) What’s the smallest number of text messages that they need to send between each other to guarantee that all eight know all the gossip?
4) What’s the smallest number of phone calls that they need to make between each other to guarantee that all eight know all the gossip?
Can you generalise this for n friends? What is surprising about the results?
Bobby is probably the best-known maths teacher in the UK. He gained fame in 2017 as a contestant on University Challenge. He continues to teach at a state comprehensive in London, but is now also a much-loved TV presenter, podcaster, numeracy campaigner and writer. His charming memoir, The Life-Changing Magic of Numbers, is out now.
He also likes to gossip, usually about the latest rumours surrounding West Ham United.
“What I like about the gossip puzzle,” he says, “is that the solution is counterintuitive. When my school students encounter problems, they will form a first impression of it. A first impression is important as it draws on our past experience. But we should be careful not to jump to a quick and incorrect conclusion.”
No gossiping, no spoilers, and I’ll be back with the answers at 5pm UK.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of Football School, a book series for 7 to 12 year olds that opens up the curriculum through football. The latest in the series, Season 4, is out in September but you can preorder now. It contains chapters on classical music, spitting, magic, the history of timekeeping, the International Space Station, etymology and much much more.
Thanks to Bobby Seagull for suggesting today’s puzzle. His book is The Life-Changing Magic of Numbers: How Maths Shapes Everyday Life. His podcast is Maths Appeal, and his new BBC Two series, Monkman & Seagull’s Genius Guide to the Age of Invention, is out in the autumn.