Multiple relationships deep

Phil, here is an example of real values:

TABLES:        Country                    Den                             Type                              Inv

FIELDS:           CountryID----------<CountryLink>--------<CountryLink  

                                                            DenID-----------------<DenLink

                                                                                                 TypeID---------???----<TypeLink

EXAMPLES:  Data Values linked to a Type record:

                        Country                    Den                             Type                              Inv

example 1:          USA--------------Dime-------------------Mercury

example 2:          Canada---------Dime-------------------Boat        

example 3:          USA--------------Dime-------------------Barber

example 4:          USA--------------Quarter----------------Barber

example 5:          Euro--------------Dime------------------ Boat

Summary of Where I Am so far:  The way my Types are linked are through the predecessor relationship files (Country and Den) serial IDs.  To record a Type, I first must select a Country (only Countries that have pre-established links to a Den are available in the pop-up menu for this field in the layout).  Once Country is selected, that then allows me to select a Den appropriate only for that Country (through a mirrored Den table).  This works well since Countries can have multiple Dens and Dens can be in multiple Countries.  Type descriptions can also be multiple ("Barber" or "Boat" in the examples above) but what makes each Type unique is not their description but their description plus their links to both Country and Den - thus each Type above is unique. (I test that each Type is unique by concatenating the Type description, CountryID and DenID into a string).

My Problem:  I am stuck getting to the next phase where I want to link an Inv record to a Type.  That is where I need to make a Type selection from the possible combinations of Country, Den and Type as noted above (I should have said a unique Type based on Type description, Country and Den).  For example, I want a Inv record linked to the example 3 combination above - Barber as Type with Dime as Den and Country as USA.  How can I get the layout to help me select the correct Type (showing a pop-up menu based on Type ID in the Inv layout only allows me to see "Barber" as my second field - but how do I know if its "Barber" from example 3 or example 4?).  I do not think a concatenated string works (I use the serialIDs for all links so they are not descriptive, plus if I used a more descriptive concatenated field, that would not be a dynamic link if the description for Country or Den was subsequently edited).

I seem so close yet I am stuck on this one....

Any help you can provide would be greatly appreciated!

A "Den" is short for a coin denomination.  "Inv" is for inventory. 

 As for Countries having multiple Dens and Dens having mulptiple Countries, I should have been more clear.  Effectively, as you more correctly note, there is a one-to-many relationship between Country and Den.  This is because each Den is unique based on the Den and Country link (in my examples, although there appear to be many "Dime" Dens linked to multiple Countries, that is not the case because each Den is unique based on the Den and Country link.  I my examples, I have a unique Den representing USA and Dime which is linked to mulitple Types.  I also have a unique Den for Canada and Dime and yet another unique Den for Euro and Dime - both of which are ulitmately linked to a Unique Type (Canada-Dime-Boat and a different Type for Euro-Dime-Boat).

Inv[entory] is a table for coins in the collection.  I can't just add a quantity field to the Denominations table because I first need to reference a Type to it so that each coin has a unique Type, Denomination and Country attached to it.  It can't simply add a quanity field to the Type table because each coin has specific attributes (grade, location, etc.) that are unique to the coin and I can multiple coins for each Type.  I built the linked tables because each table has plenty of underlying data specific to Country, Denomination and Type that I would want each coin in the Inv table to be able to reference.

Ok - I see your point as to the proper relationship link and now I am on the right track as to the tables and relatinships.  But how on the Inventory layout do I pick the requisite Denomination link that is also appropriately linked to both Country and Type (I need to be able to see a main description from all three linked tables to do the job by choosing the right combination of all three as in any of the examples shown)?  That's where I get stuck.