How come my cisco router doesn't accept an address like:
        "ip address 192.111.107.1 255.255.255.240"
or      "ip address 171.69.0.1 255.255.0.0"

When "subnetting" of IP networks was first sanctioned by the IETF, the first
and last subnets (the all zeros subnet and all ones subnet) were reserved for
rather obscure uses and because of the confusion that would be caused with
routing protocols that don't carry net mask information.  It was technically
illegal to place hosts or routers on those two subnets.

Several hosts and most other vendor's router products have problems operating
with the reserved subnets,  so their use is discouraged.  However, in 1995,
the IETF removed the restrictions on the use of these reserved subnets as part
of the classless routing effort.

If you would like to use the reserved subnets, simply add the line
"ip subnet-zero" to your cisco configuration.

You might consider adding "ip subnet-zero" to all your configurations as a
metter of course, to avoid being bitten by this in the future.