Question 70
Albert, Ben and Carla are looking at the dust in the air, and Ben says that if there are $1000$ dust grains in a $10\text{cm} \times 10\text{cm} \times 10\text{cm}$ box, then no matter how they are situated, he can choose a point such that there are at least $10$ dust grains in a distance of at most $2$ cm from the point, but Albert does not believe him. Carla says that no matter how the dust grains are situated, she can choose a point such that there are at least $10$ dust grains in a distance of at most $2$ cm and at least $1$ cm from the point, but Ben does not believe her. Determine who is right, Albert, Ben or Carla.