I am only doing this because I believe you. The kids I am going to school with are lost, and we are using the cisco netacad curriculum. The answer is divide and conquer. Assuming I counted correctly this is correct, though I would have taken more time to look at how the routes will aggregate. There are gaps if you need to fix something. It took longer to count than to produce this.
Network Net Broadcast CIDR Mask UsableHosts
172.16.0.0 172.16.63.255 18 255.255.192.0 16,382 AVL isPrivate, isClassB
172.16.64.0 172.16.95.255 19 255.255.224.0 8,190 AVL isPrivate, isClassB
172.16.96.0 172.16.127.255 19 255.255.224.0 8,190 REQ 8000 isPrivate, isClassB
172.16.128.0 172.16.143.255 20 255.255.240.0 4,094 AVL isPrivate, isClassB
172.16.144.0 172.16.159.255 20 255.255.240.0 4,094 REQ 4000 isPrivate, isClassB
172.16.160.0 172.16.175.255 20 255.255.240.0 4,094 REQ 4000 isPrivate, isClassB
172.16.176.0 172.16.191.255 20 255.255.240.0 4,094 REQ 4000 isPrivate, isClassB
172.16.192.0 172.16.207.255 20 255.255.240.0 4,094 REQ 4000 isPrivate, isClassB
172.16.208.0 172.16.223.255 20 255.255.240.0 4,094 REQ 4000 isPrivate, isClassB
172.16.224.0 172.16.227.255 22 255.255.252.0 1,022 AVL isPrivate, isClassB
172.16.228.0 172.16.231.255 22 255.255.252.0 1,022 REQ 1000 isPrivate, isClassB
172.16.232.0 172.16.235.255 22 255.255.252.0 1,022 REQ 1000 isPrivate, isClassB
172.16.236.0 172.16.239.255 22 255.255.252.0 1,022 REQ 1000 isPrivate, isClassB
172.16.240.0 172.16.243.255 22 255.255.252.0 1,022 REQ 1000 isPrivate, isClassB
172.16.244.0 172.16.245.255 23 255.255.254.0 510 AVL isPrivate, isClassB
172.16.246.0 172.16.247.255 23 255.255.254.0 510 REQ 500 isPrivate, isClassB
172.16.248.0 172.16.249.255 23 255.255.254.0 510 REQ 500 isPrivate, isClassB
172.16.250.0 172.16.250.255 24 255.255.255.0 254 REQ 250 isPrivate, isClassB
172.16.251.0 172.16.251.255 24 255.255.255.0 254 REQ 250 isPrivate, isClassB
172.16.252.0 172.16.252.255 24 255.255.255.0 254 REQ 200 isPrivate, isClassB
172.16.253.0 172.16.253.255 24 255.255.255.0 254 REQ 200 isPrivate, isClassB
172.16.254.0 172.16.254.127 25 255.255.255.128 126 AVL isPrivate, isClassB
172.16.254.128 172.16.254.255 25 255.255.255.128 126 REQ 125 isPrivate, isClassB
172.16.255.0 172.16.255.127 25 255.255.255.128 126 REQ 125 isPrivate, isClassB
172.16.255.128 172.16.255.191 26 255.255.255.192 62 AVL isPrivate, isClassB
172.16.255.192 172.16.255.199 29 255.255.255.248 6 AVL isPrivate, isClassB
172.16.255.200 172.16.255.203 30 255.255.255.252 2 AVL isPrivate, isClassB
172.16.255.204 172.16.255.207 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.208 172.16.255.211 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.212 172.16.255.215 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.216 172.16.255.219 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.220 172.16.255.223 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.224 172.16.255.227 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.228 172.16.255.231 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.232 172.16.255.235 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.236 172.16.255.239 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.240 172.16.255.243 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.244 172.16.255.247 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.248 172.16.255.251 30 255.255.255.252 2 REQ 2 isPrivate, isClassB
172.16.255.252 172.16.255.255 30 255.255.255.252 2 REQ 2 isPrivate, isClassB