# Problem 3

# Lower bound for number of passengers

**Due**: January 19

**Points**: 2

In the "airplane bomber" scenario, we are assuming that:

- There are 200 passengers total.
- At least 20 passengers must collude to make a bomb.
- At least 999 out of 1000 times, not a single passenger will have any bomb-making liquid.

Prove that *any* deterministic algorithm that screens at most 180 passengers (even in a single case) may result in 1/1000 planes being blown up.