To guess or figure something out by intuition
Encoding Strategies:
linguistic

a-
to
+
divine
god-like
+
-ar
verb suffix
Adivinar means to guess and is built on the English word divine1: when you guess something you can't possibly know, it's as if the answer came straight from the gods. This is also where the English verb "to divine" comes from, as in divining the future or divining for water.
adivinar
to guess
To divine the right answer when you can't know it for sure.
Adivina cuántos caramelos hay en el frascoGuess how many candies are in the jar
¡Adivina qué! Nos vamos a MéxicoGuess what! We're going to Mexico
to predict, to foretell (the future)
To divine the future, fortune-teller style.
La adivina dice que puede adivinar el futuro leyendo las cartasThe fortune teller says she can predict the future by reading cards
Nadie pudo adivinar cómo terminaría la historiaNo one could foretell how the story would end
to sense, to discern (something hidden)
To divine what's hidden from small clues, like reading someone's intentions.
Por su sonrisa, adiviné que traía buenas noticiasFrom her smile, I sensed she was bringing good news
Adivinó la tristeza detrás de mis palabrasShe discerned the sadness behind my words
adivinarse
to make out (faintly)
The reflexive here means "it can be guessed": something too faint to really see, so you guess at it as much as you see it.
A lo lejos se adivinaba la silueta de las montañasIn the distance you could just make out the silhouette of the mountains
Entre la niebla se adivinaban las luces del puertoThrough the fog you could just make out the lights of the harbor