I very often read things like chmod 777 <somefile>.
Well, I understand chmod +x <somefile>, but so far, I haven't been able to figure how to compute these numbers. Is there anyone who knows?
Thank you a lot

break it down like this in a nutshell:

777 : the first 7 stands for user, second one stands for groups, and the third stands for everyone or world.

Now the 7 indicates that it has a value to give rwx permissions.. so that is read, write and execute.

It is the total of each individual permission..

Read = 4
Write = 2
Execute = 1

Say you wanted a permission level of 640, that would mean that the user has Read/Write permission, the group has read permission and everyone else has no permissions.

some examples:

640 = rw-r-----
755 = rwxr-xr-x
777 = rwxrwxrwx

So basically its just adding the values for the permissions settings of each individual read, write or execute on any given group or user..

Hope this helps.. in a way. Ask if you have any questions.

If you know binary numbers representation you'll get it by snap
Computers only understand 0 or 1 (low/high, whatever you prefer, let's not get adventurous into computer science field), so 1 will be for turning the bit on and 0 to turn it off
so you have 777 (7 for owner, 7 for group and 7 for others)
lets make every digit in binary, so 7 decimal is 111 in binary
(1x2 in power of 2 plus 1x2 in power of 1 plus 1x2 in power of 0) == (4+2+1=7)
each number represents read (r) write (w) and execute (x) permissions
so 777 translates into
111 111 111
rwx rwx rwx

Lets turn off some permissions
100 000 001
r-- --- --x
lets make it decimal now
100 is 1x 2 in power of 2 + 0x 2 in power of 1 + 0x 2 in power of 0 equals 4
000 is 0
and
001 is 1
----------
so chmod 401 will yeild these permissions
Got it?
Danm, I feel like a prof in a college :-)

The chmod numbers are represented in the octal number system. That's why you won't see a single digit larger than 7.

Yeah you are right, I was too into professor/student stuff
My bad.

Thank you all for the detailed answers - it's easier than I would have thought - and thinking of it in binary makes it very easy
Thank you all