Random Puzzles 

Workings

Hints
The first letters of the words are: T, C, C, G, T, B, S, B, D, G.

Answers
----rem = theorem ----oct = concoct ----pso = calypso ----dma = grandma ----edo = torpedo ----rre = bizarre ----sfy = satisfy ----ott = boycott ----hma = drachma ----dpa = grandpa

Workings

Hint
There is more than one answer.

Answers
Common words:

hate, late, lane, lone, love
hate, have, hive, live, love
hate, date, dote, dove, love
hate, rate, rote, rove, love
hate, have, wave, wove, love
hate, have, cave, cove, love

Less common words:

hate, late, lave, love
hate, have, hove, love
hate, mate, mote, move, love

Workings

Hint
There are 60 seconds in a minute, and 60 minutes in an hour.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 60 x 24 x 365 = 525,600 minutes in a (non-leap) year.

Workings

Hint
How many 2 x 2 squares are there?

Answer
There are 128 squares without a rook.

Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are  6 squares of size 4 x 4.
There is   1 square  of size 5 x 5.

Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.