Math Playground
Activities

Is Your Secret Safe? Think Exponentially

Tell two friends — how fast does a secret spread?

You tell a secret to two friends. Each tells two more. Each of those tells two more. After 10 rounds, how many people know?

Try this
10
people who know after r rounds = 2ʳ = 1024

Doubling is deceptively fast

After 1 round, 2 people know. Round 10: over a thousand. Round 20: more than a million. Round 30: a billion. Nothing about telling 'just two friends' feels dangerous — until the doubling has had a few rounds to build momentum that no one can outrun.

This is the maths behind viral rumours, chain messages and gossip. It's also exactly how compound interest, bacterial growth and pandemics behave — the same curve, different costume.

Your turn

If each person who hears the secret tells 2 new people, how many people know after 15 rounds?

Exponential growth

After 10 rounds, over a thousand people. After 20, a million.

This is why secrets don't stay secret. Doubling builds momentum that no one can outrun.