Solution:

If the man killed himself, he would not have been able to rewind the cassette. Thus it is clear someone else killed him.

Solution:

f the last elf is taking some time to answer the question then it shall mean that the elf's before him are all wearing distinct coloured hats. However sufficient time shall be given to the last elf to give the answer.
If he views the similar coloured hats in front of him , he shall quickly tell the answer

Solution:

Flyball should pay Lavy $11 instead of accepting his counter offer as in that case the club will end up paying almost double the amount.

Solution:

Hockey Stick $49.50 & ball $0.50

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

20
Just count the nines in the numbers: 6, 16, 26, 36, 46, 56, 76, 86, 96, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69.
Note: 66 contains TWO nines

Solution:

Old password : altered

New Password : distinct

Solution:

LOTTO

Explanation:
Just flip the two rows 1 and 2 vertically, you will find the word "Lotto".

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

zero

I had 3 green socks and 1 Pink sock.

=> chances of pair of green socks = 1/2
chances of pair of mixed socks = 1/2
chances of pair of green socks = NULL

Solution:

It can be done in 8 moves as shown in the animated image below.