In German, the word that represents trying to find the right answer to a question, by selecting the most plausible option is raten. Germans have a separate word for the act of doing so correctly: erraten.
The word raten also has another meaning in German: to give councel/advice. So, in order to distinguish raten from its alternate meaning of “to give advice”, the accusative is used (rather than the dative).
Bonus Words
If you want to get more specific, you can use a few other words for “to guess”. For example, vermuten means “to assume”, schätzen means "to estimate”, annehmen "to suppose”, and ahnen “to suspect”
German that fits into your busy life.
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Examples
Du hast es erraten! You guessed it!
Er hat mein Gewicht erraten. He guessed my weight.
Ich weiss es nicht. Ich muss raten. I don’t know. I have to guess.
Ich vermute, dass sie später kommen werden. I assume they will come later.
Ich schätze die Temperatur auf etwa 5 Grad. I guess the temperature is about five degrees.
Ich nehme an, dass es möglich ist. I suppose it’s possible.
Nichts ahnend ging er in das Haus. Without suspecting anything he went into the house.