Answer:
11 bits
Step-by-step explanation:
A Class B network, such as the one described in the question, has an address range of 172.16.0.0 to 172.31.255.255. In order to use a single subnet mask throughout the network, the engineer must choose a mask that provides enough subnet bits to support 1000 subnets while also allowing for a large number of hosts per subnet.
The largest number of hosts per subnet is provided by a mask with the fewest number of subnet bits. However, this would not be sufficient to support 1000 subnets. Therefore, the engineer must choose a mask that provides a balance between the number of hosts per subnet and the number of subnet bits.
One possible mask that meets these criteria is 255.255.248.0. This mask provides 21 subnet bits, which is enough to support up to 2^21 = 2097152 subnets. It also provides 11 host bits, which allows for up to 2^11 = 2048 hosts per subnet. This is the largest number of hosts per subnet among the masks considered by the engineer, while also providing enough subnet bits to support 1000 subnets.