Is there a situation with IP addressing where a subnet mask like 250.255.112.0 is legal?
No. Think of the subnet mask as a string of 32 bits. Valid subnet masks should start with one bits, then switch at some point to zero bits and end that way. The first number in this example (250 decimal), translates in binary as 11111010. Notice that it switches to zero, then back to one, then back to zero again. 250 is not a valid component in a subnet mask. To put it another way, only nine numbers may legally appear in a subnet mask – 0, 128, 192, 224, 240, 248, 252, 254, and 255. Furthermore, three of the four numbers used in any subnet mask must be either 0 or 255. The mask must start with zero or more 255s, then possibly one of the other numbers (but only one), and then end with zero or more 0s.
