When it's bad luck to meet a black cat?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

There are are five things wrong with this sentence; only geniuses will be able to to spot all of the mitstakes

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Role Action
Block Prevents the target player from acting
Redirect Change target player target.
Save Protects the target player from death.
Seer Sees all actions that occurred
Murderer Kills the target player

The following five players are playing:

Andy
Brian
Chris
Daniel
Fred

You are Andy the Seer and you saw the following things:
a) Brian was redirected to Chris.
b) Chris was blocked.
c) Daniel was killed.

Who is the murderer then?

He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?