Present Perfect & PP Continuous Intermediate

At last! I ______(solve) the problem!

Oh, there you are. I __________(look) for you everywhere!

I ______(never/understand) Maths and Physics.

I ______(believe) he was innocent from the beginning.

John ______(never/see) this film before.

I'm sorry. Monica is not here. She ______(go) out.

The children are tired because they __________(play) all day.

I _______ (write) emails since 5 o'clock this morning.

I _____ (know) Peter for a long time.

My brother ______(buy) a new motorbike. It looks great.