"encontrarse con" is a phrasal verb.
Phrasal verbs are the combination of a verb plus a preposition that forms a single semantic unit. The preposition which is added may change the verb in a subtle way, or it may completely change the meaning.
Spanish, like English, has a lot of phrasal verbs, and you just have to learn them.
For example, in English, think of "to run", which forms many phrasal verbs which have little or nothing to do with the physical action of running...
"He RAN INTO an old friend"
"She RAN OVER the bicycle in the driveway"
"We RAN THROUGH our lines at rehearsal"
"He RAN AWAY at the age of 14"
"She RAN UP a large bill at the hotel"
"I have RUN OUT of examples"
Jonbriden explained what phrasal verbs were, and rspreng confirmed what Jon said. Perhaps you are interpreting the Spanish too literally because you are focusing too much on the particle "con." Particles are defined as prepositions that adverbially alter a verb's meaning when they are used immediately after the verb.
Also, when a preposition is used as a particle, its meaning and its usage are subordinated to the overall meaning of the entire verb phrase (that is, subordinated to the verb + the particle). That's why "encontrarse con" can be translated as "to run into." That's the way colloquisms work: they don't translate word for word, but it's grammatical Spanish and typically how native speakers string the phrase together. Once I accepted that you have to embrace colloquialisms, I started learning much faster.
In other words, the definition of "encontrar" changes from "to find/to meet/to encounter" into the colloquial definition of "encontrarse + con," which is "to run into/to bump into/to stumble upon." Most words have more than one meaning, no matter what the language, so sometimes, when one interpretation doesn't work–that is, translating "se habrán encontrado" as "they will have found"–you just have to find an alternate translation that does. Myself, I like "They will have run into problems." The key to this translation is the colloquial use of the particle "con."
Somewhere in the Duo algorithm, "come across" must be accepted for as a translation for "encontrado," just as "met with" is acceptable as a translation of "encontrado." Thus, the program is just combining the prepositional particles "with" and "across" in order to get feedback so that "come across with" can be either incorporated as acceptable or eliminated because it is unacceptable.
Also on the other side of the Atlantic it can be used without "con". This sentence is just an example, as far as I understand it, and the main point would be the phrasal verb "encontrarse con" something or somebody. This can be translated as "stumbled upon" or "discover". Without "con" you leave it just as "found"
In some context the preposition may be removed, but the context change... here there is no context. That is sometimes confusing.
Cuando finalmente llegamos a su casa, nos encontramos con que se había ido ya When we finally arrived to his place, we found out he had just left
Hemos seguido tus indicaciones, pero nos encontramos con que había obras (con and que could be removed and the sentence won't change significantly in meaning)
Nos encontramos con Jose en la calle (also nos encontramos a Jose) the difference is that with "con" has a meaning of stumbling upon or unplanned meeting.
Cuándo ud. me dice – Hemos seguido tus indicaciones, pero nos encontramos había obras – ¿Es las palabra obras se traduce como fábrica, planta, o edifício industrial?al?
When you tell me "We followed your directions, but we found there were works," is the word obras translated as factory, plant, or industrial building?
Future perfect in Spanish also can translate in life (if not in Duoling) as "must have" - for example: They're late. They must have had problems as "Ya no han llegado. Se habrán encontrado (con) problemas." Just like future can mean "could", as in "¿Quién será, tocando a mi puerta a estas horas?" - "Who could it be, calling (knocking at my door) at such hours?"
Amazingly, however, Duolingo DOES catch a lot of natural speech...
I believe that the Duo algorithm provides the most popular responses as possible translations, which makes sense when you consider that both of the suggested "correct" solutions use "found" instead of "encountered" as the translation. I suspect that the verb "found," having a broader definition than the verb "encountered," is most often used as an "educated guess."
In reality, however, "encontrado" is better translated as "encountered." "Encountered" means "to come across" (to notice something or someone while you are doing something else), "to meet with" (in the sense of bumping into, running into, or meeting another unexpectedly), and "to find" (to discover).
The denotative meanings of "trouble" and "problems" call for the word "problemas" to be translated as "problems" rather than as "trouble" because while any "trouble" is a "problem," not all "problems" are "trouble." Besides, since the Spanish sentences uses the word "problemas," it's better to stick with the word that can be easily translated literally and then find the verb translation that goes best with "problemas." IMO, therefore, the best translation is "Se habrán encontrado con problemas"/"They will have met with problems" or "They will have come across problems."
It's not correct because "encontrarse + con" is a colloquialism. BTW, just wanted to add that the difference between a colloquialism and an idiom is very slight. Both are concatenations that native speakers accept as part of the language and frequently use. However, colloquialisms are usually grammatical, while idioms are usually grammatically deficient in some way, such as spelling, odd verb choices, or nonstandard word order.
So, I have read some excellent clarifications on how encontrarse con doesn’t mean find with, but rather run into. But above DL’s translation is found. So I am marking their translation as incorrect. My translation was also incorrect, so thanks very much for the explanation because DL’s usage just confused me further.
This translation makes absolutely no sense. The Spanish future tense is used here to express probability. In English, I would say, "They must have run into problems" / "They must have had problems". Nothing about this sentence suggestions that it refers to an actual future time period...
It seems straight forward:
encontrarse + con is to find oneself, his self, her self, themselves, etc. with
Example: Me habré encontrado con problemas. - I will have found myself with problems. (Problems pertaining to myself)
As opposed to:
Habré encontrado problemas. - I will have found problems. (Problems not of myself)
They will have found themselves with problems. - Accepted by Duo.