Special Permissions Linux

I’ve been working on a Linux privilege escalation problem that involves special permissions, specifically the setuid bit. The question I’m trying to answer is “Find a file with the setuid bit set that was not shown in the section command output (full path to the binary).”

I ran the suggested command find / -user root -perm -4000 -exec ls -ldb {} \; 2>/dev/null and found a file that wasn’t shown in the command output, which is /usr/bin/facter. I’m unsure if the answer is supposed to include the full path with the root directory, or if /usr/bin/facter is sufficient.

I’ve been working on this for 8 hours and I’m feeling exhausted. If anyone can provide any guidance or clarification, I would greatly appreciate it.

Edit: I’ve solved it. You just need to look carefully at the outputs.

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Thank you.
Im tired. I did not see it for a long time.

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Thanks a lot for B.
If you really can’t find a clue, you can try to enumerate the output of find