root
user can write to a file even if its write
permissions are not set.
root
user can read a file even if its read
permissions are not set.
root
user can cd
into a directory even if its execute
permissions are not set.
root
user cannot execute a file when its execute
permissions are not set.
Why?
user$ echo '#!'$(which bash) > file
user$ chmod 000 file
user$ ls -l file
---------- 1 user user 12 Jul 17 11:11 file
user$ cat file # Normal user cannot read
cat: file: Permission denied
user$ su
root$ echo 'echo hello' >> file # root can write
root$ cat file # root can read
#!/bin/bash
echo hello
root$ ./file # root cannot execute
bash: ./file: Permission denied
Best Answer
In short, because the execute bit is considered special; if it's not set at all, then the file is considered to be not an executable and thus can't be executed.
However, if even ONE of the execute bits is set, root can and will execute it.
Observe: