It has taken 21 years to get mobile phones into the hands of 3 billion people around the world. Reaching the next 1.5 billion, who live in the world’s poorest and most remote corners, is expected to take a lot less time but will pose much tougher challenges. There is, for instance, the thorny question of how to justify the expense of installing transmission towers in areas where people can only afford to pay as little as $2 per month for phone service — not to mention the cost of running and servicing equipment where electricity and engineers are in short supply.