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I'm very surprised by this, because manually I was able to deterministically without guessing reach 5 missing DT-combinations. And the last 5 shouldn't take long time to determine a possibility for.
Can someone else give this a try while GreyHams is away? Otherwise I'll wait. Have fun with your Jasmer GreyHams :)

I don't know how exactly you've tried programming it, but I've tried writing some pseudocode for how I would program what I did manually:

Initialize a result matrix
Initialize a cache list for possible caches that hasn't been added yet
Start loop
____Take the country with the fewest number of finds
____For each cache in that country with a missing DT-combination, add it to the cache list if a similar cache hasn't
____already ____been added to the list (similar meaning same country, type and DT)
____Call check_country with that country
Loop until there's no more countries
Start guessing and backtracking with the remaining possibilities. Start with the country types with the fewest possibilities and/or the DT-combinations with the fewest possibilities
Before each guess check if there's any country types or DT-combinations with only one possibility that can be safely added

check_country(country)
If the country has less than 4 types in the cache list:
____For the types, where the country has exactly one cache in the cache list:
________Add the cache to the result matrix
________Delete all caches in the cache list with that DT-combination
________For each country with a deleted cache call check_country with that country

I'm very surprised by this, because manually I was able to deterministically without guessing reach 5 missing DT-combinations. And the last 5 shouldn't take long time to determine a possibility for.
Can someone else give this a try while GreyHams is away? Otherwise I'll wait. Have fun with your Jasmer GreyHams :)

I don't know how exactly you've tried programming it, but I've tried writing some pseudocode for how I would program what I did manually:

Initialize a result matrix
Initialize a cache list for possible caches that hasn't been added yet
Start loop
____Take the country with the fewest number of finds
____For each cache in that country with a missing DT-combination, add it to the cache list if a similar cache hasn't already ____been added to the list (similar meaning same country, type and DT)
____Call check_country with that country
Loop until there's no more countries
Start guessing and backtracking with the remaining possibilities. Start with the country types with the fewest possibilities and/or the DT-combinations with the fewest possibilities
Before each guess check if there's any country types or DT-combinations with only one possibility that can be safely added

check_country(country)
If the country has less than 4 types in the cache list:
____For the types, where the country has exactly one cache in the cache list:
________Add the cache to the result matrix
________Delete all caches in the cache list with that DT-combination
________For each country with a deleted cache call check_country with that country