Random Puzzles 

Workings

Hint
The first letters of the words are: B, A, S, A, B, B, R, N, B, C.

Answer
BINARY = BRAINY
ABROAD = ABOARD
RASCAL = SCALAR
ALTARS = ASTRAL
BADGER = BARGED
BARKED = BRAKED
MARBLE = RAMBLE
UNABLE = NEBULA
TABLET = BATTLE
CALLER = CELLAR or RECALL

There are some less common anagrams such as:
RASCAL = SACRAL
ALTARS = TARSAL
ALTARS = RATALS
ALTARS = TALARS
BADGER = GARBED
BARKED = DEBARK
MARBLE = BLAMER
MARBLE = AMBLER
MARBLE = LAMBER
UNABLE = UNBALE
TABLET = BATTEL

So you can have an extra half point if you found one of these! There are some even rarer anagrams, but I don't think I'll allow those!

Workings

Hint
How many mice does one cat catch?

Answer
Six mice.

  1.5 cats catch 1.5 mice in 1.5 days.

so

  1 cat catches 1 mouse in 1.5 days.

  1 cat catches 2 mice in 3 days.

Therefore

  3 cats catch 6 mice in 3 days.

Workings

Hint
Where on Earth can you end up back where you start?

Answer
White.

They were at the north pole and saw a polar bear.

Workings

Hint
This is a well known nursery rhyme.

Answer
HDD.

The initial letters from the nursery rhyme, Hickory Dickory Dock.
Hickory, dickory, dock,
The mouse ran up the clock,
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.