Unable to install R base; unmet dependencies on Ubuntu 18.04 [duplicate]

I am trying to install R on an Ubuntu 18.04 machine and am encountering an "unmet dependencies" problem. However, I am unable to determine where I can go or what I need to fix on my system to overcome this. Any help would be greatly appreciated.

I am running Ubuntu 18.04.2 LTS (with 16Gb RAM and 500Gb hard disk), using just the standard bionic repositories; the only PPA i've added is that for libreoffice. To see what's there, the output to sudo apt update is

Ign:1 http://dl.google.com/linux/chrome-remote-desktop/deb stable InRelease
Ign:2 http://dl.google.com/linux/chrome/deb stable InRelease   
Hit:3 http://dl.google.com/linux/chrome-remote-desktop/deb stable Release
Hit:4 http://dl.google.com/linux/chrome/deb stable Release                 
Get:7 https://desktop-download.mendeley.com/download/apt stable InRelease [2,456 B]
Get:8 https://typora.io/linux ./ InRelease [758 B]                         
Hit:9 http://repository.spotify.com stable InRelease                       
Hit:10 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ InRelease
Hit:11 http://ppa.launchpad.net/libreoffice/ppa/ubuntu bionic InRelease    
Hit:12 http://sg.archive.ubuntu.com/ubuntu bionic InRelease                
Hit:13 http://sg.archive.ubuntu.com/ubuntu bionic-backports InRelease
Get:14 http://sg.archive.ubuntu.com/ubuntu bionic-security InRelease [88.7 kB]
Fetched 91.9 kB in 3s (26.5 kB/s)    
Reading package lists... Done
Building dependency tree       
Reading state information... Done
All packages are up to date.

(I try to keep things in sync as much as possible and run sudo apt update && sudo apt upgrade at least once every two days.)

When I attempt to install the first of R's components r-base (via sudo apt install r-base) I get the following unmet dependencies:

Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 r-base : Depends: r-base-core (>= 3.4.4-1ubuntu1) but it is not going to be installed
          Depends: r-recommended (= 3.4.4-1ubuntu1) but it is not going to be installed
          Recommends: r-base-html but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

Running software-properties-gtk, I see that all repositories are enabled. Running sudo apt-get clean and sudo apt-get autoclean proceeds to completion with no error messages. When I execute

$ sudo apt-get -f install
$ sudo dpkg --configure -a
$ sudo apt-get -f install

the output is

Reading package lists... Done
Building dependency tree       
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

so there seems to be no held or conflicted or broken packages on my system. I have also executed sudo apt --fix-broken install, but again, as above, my system seems to have no held or broken packages.

Running sudo apt-get dist-upgrade shows

Reading package lists... Done 
Building dependency tree 
Reading state information... Done 
Calculating upgrade... Done 
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

I'm happy to try anything else someone might want to suggest to see if the fault remains on my system.

Next I add

deb https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/

to my /etc/apt/sources.list and run

$ sudo apt update
$ sudo apt install r-base

Still no joy; the output is now (omitting repeats from above)

The following packages have unmet dependencies:
 r-base : Depends: r-base-core (>= 3.6.0-2bionic) but it is not going to be installed
          Depends: r-recommended (= 3.6.0-2bionic) but it is not going to be installed
          Recommends: r-base-html but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

(but at least I've moved from 3.4.4-1ubuntu1 to 3.6.0-2bionic.) Repeating the sudo apt-get -f install ; sudo dpkg --configure -a; sudo apt-get -f install sequence above continues to show

Reading package lists... Done
Building dependency tree       
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

so again there seems to be no held or conflicted packages otherwise.

The output from apt-cache policy r-base is:

  Installed: (none)
  Candidate: 3.6.0-2bionic
  Version table:
     3.6.0-2bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.6.0-1bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.5.3-1bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.5.2-1bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.5.1-2bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.5.1-1bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.5.0-1bionic 500
        500 https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/ Packages
     3.4.4-1ubuntu1 500
        500 http://sg.archive.ubuntu.com/ubuntu bionic/universe amd64 Packages
        500 http://sg.archive.ubuntu.com/ubuntu bionic/universe i386 Packages

I'm not sure, however, where to go dig further or what files to adjust based on this output.

Are there locations I need to add to my /etc/apt/sources.list to put in place the dependencies on r-base-core and r-recommended? Where else do I need to go to get them? The linux installation page

https://cran.ma.imperial.ac.uk/bin/linux/ubuntu/README.html

does not suggest to me anything further to add to my /etc/apt/sources.list. Google returns a whole bunch of other things including marutter's PPA and I've experimented with adding those into my sources, but none has allowed me to install to completion. [Yes, when I've removed them, I've made sure to run through clean and autoclean each time, as above.]

To be clear, I am not obsessed about having the absolutely latest version of R/ I'd be happy with anything else slightly out-dated too, but I don't see any hint on the linux installation page for R what I might adjust.

(On my other machines, GalliumOS 2.1 and GalliumOS 3.0, I have installed R and RStudio, no issues. )

Any help would be greatly appreciated.

(This problem has now been solved as described below; I had two slightly inconsistent versions of packages. I ended up removing both and re-installed just one.)

I became convinced, after following the chain of fails on a number of the pathways, — "going down the rabbit hole", as suggested by @user535733 — that somehow two different sources appeared to have crept onto my system, each individually providing a consistent complete set of packages, but across the both mutually incompatible. An instance of that was finding gcc-8-base referring to both 8.3.0-6ubuntu1~18.04 and 8-20180414-1ubuntu2, but there were others, eventually found to be too many to resolve one at a time.

So I removed and restored the default repositories, as in, e.g., How do I restore the default repositories? through moving /etc/apt/sources.list to some safe temporary place [to be discarded later after everything was seen to work], touch-ing to create a new empty version, and then using software-properties-gtk to provide a fresh set of Ubuntu Software sources, and Updates (security and updates channels). Closed that so the system updated, and then in a terminal I ran

$ sudo apt update && sudo apt upgrade
$ sudo apt install r-base # Works cleanly!

(Many thanks to everyone who helped, but most of all to @user535733)