Which of the following network design elements allows for many internal devices to share one public IP address?

This should be NAT…

The majority of NATs map multiple private hosts to one publicly exposed IP address. In a typical configuration, a local network uses one of the designated “private” IP address subnets (RFC 1918). A router on that network has a private address in that address space. The router is also connected to the Internet with a “public” address assigned by an Internet service provider. As traffic passes from the local network to the Internet, the source address in each packet is translated on the fly from a private address to the public address. The router tracks basic data about each active connection (particularly the destination address and port). When a reply returns to the router, it uses the connection tracking data it stored during the outbound phase to determine the private address on the internal network to which to forward the reply

http://en.wikipedia.org/wiki/Network_address_translation – it’s NAT

There are three types of NAT: static NAT, Dynamic NAT (AKA Pooled NAT), and NAT Overloading (AKA PAT). PAT multiplexes the gateway’s public IP address through the use of the TCP or UDP ports being used when communications are returned from foreign systems (for example, someone else’s webserver). This gives PAT (AKA NAT Overloading) a many-to-one relationship (one public IP address used many times at once). The other two NATs (static and dynamic) use a one-to-one relationship. The LAN client borrows the public IP address, but the IP address can’t be used again until the client’s conversation ends. After which the public IP address is placed back in the pool.

DNAT = dynamic NAT which means you’d need to have a pool of public IP addresses to be tied with the internal IP addresses. So to only use ONE public IP address, you’d need to use PAT. The ONE public IP address statement is the key.