to fall for / fail / drop in
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to fall for
Colloquial for: to let oneself be deceived by someone or something; to fall victim to a scam or trick.
Ich kann nicht glauben, dass ich auf diesen alten Trick reingefallen bin.
I can't believe I fell for that old trick.
to fail
Colloquial for: to fail an exam or test.
Er hat hart gelernt, ist aber trotzdem in der mündlichen Prüfung reingefallen.
He studied hard, but still failed the oral exam.
to fall into
Literal: to unintentionally fall into something.
Pass auf, dass du nicht in die tiefe Pfütze reinfällst!
Watch out that you don't fall into the deep puddle!
to drop in
Colloquial for: to visit someone without notice and often unexpectedly.
Gestern Abend sind unsere Nachbarn einfach so bei uns reingefallen.
Last night our neighbors just dropped in on us out of the blue.
'Reinfallen' (to fall for / fail / drop in) is a separable verb. The prefix 'rein' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er fällt immer auf dieselben Witze rein.
He always falls for the same jokes.
Since 'fallen' (to fall) describes a movement or a change of state, the perfect tense of 'reinfallen' is always formed with the auxiliary verb 'sein'.
Leider bin ich in der Fahrprüfung reingefallen.
Unfortunately, I failed the driving test.
The figurative meanings—being deceived, failing an exam, or visiting spontaneously—are all colloquial. Only the literal meaning 'in etwas hineinfallen' (to fall into something) is stylistically neutral.
Er ist auf ein gefälschtes Angebot im Internet reingefallen.
He fell for a fake offer on the internet.
When 'reinfallen' means 'getäuscht werden' (to be deceived), it is always used with the preposition 'auf' and the accusative. You fall 'auf' a trick, a scam, or a person.
Fall nicht auf seine leeren Versprechungen rein!
Don't fall for his empty promises!
In the meaning 'nicht bestehen' (to fail), 'reinfallen' is often used with the preposition 'in' and the dative. You fail 'in der Prüfung' or 'im Examen' (in the exam).
Sie hat Angst, in der mündlichen Prüfung reinzufallen.
She is afraid of failing the oral exam.
to occur to / collapse / invade
The supplied visit context is not supported for einfallen by its accepted meanings. Reinfallen, on the other hand, can colloquially refer to dropping in on someone without notice, so einfallen cannot be used here as a word with the same meaning.
Nach der Arbeit wollte ich unangemeldet bei meiner Freundin reinfallen.
After work, I wanted to drop in on my girlfriend without notice.
Mir fiel plötzlich ein, dass ich heute noch meine Freundin anrufen wollte.
It suddenly occurred to me that I still wanted to call my girlfriend today.
