Two friends pass blank public cards across a bridge watched by a small robot while face-down private cards stay at their desks.

Can friends make a secret on a public line?

tap the public bridge

Ana and Bo cannot whisper or meet. Every card they send crosses a public bridge where a listener copies it. Can they end with the same hidden number without sending that number?

the public machine

Start at 1. Choose a multiplier.

Each hop multiplies by your chosen card, then keeps the remainder after dividing by 17. Repeat for your hop count.

try the forward machine

Make a public card with ×3

unrelated practice count1 hop → landing 3
1 hop4 hops

Start at 1, use multiplier 3, and repeat. The friends’ private counts are still unknown.

build on two sides

Private cards stay home

Start at 1 · ×3 · private count unknown (1–16)
the listener's notebook

Everything that crossed is here

Is that transcript enough to recover the covered spot anyway?

Public: mod 17 · ×3 · 15 · 6. Private cards: covered.

On this tiny toy, what happens when the listener tries?