How to trace the routes to all hosts in a subnet?

Solution 1:

There is no such thing available. Almost always all IPs in same block are using same routes (typical routing works with subnet masks).

In Linux, you can use short script, for example

for i in $(seq 1 255); do
 traceroute 10.10.16.$i
done

This prints route to each address, and do not include any comparing functions to detect different routes to different addresses.