Solution:

14

Explanation
If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.

Solution:

A and W.

The letters are the first letters of the words in the question. Thus, the next two letters are A and W.

Solution:

BACK

All the others can also be read backwards as proper words.

Solution:

61

Reversed digits of squares of number in descending order.

Solution:

Submarine

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200

Solution:

3211000

Solution:

Simple strategy: Elect one person to be the guesser, the other two pass. The guesser chooses randomly 'green' or 'blue'. This gives them a 50% chance of winning.


Better strategy: If you see two blue or two green hats, then write down the opposite color, otherwise write down 'pass'.

It works like this ('-' means 'pass'):

Hats: GGG, Guess: BBB, Result: Lose
Hats: GGB, Guess: --B, Result: Win
Hats: GBG, Guess: -B-, Result: Win
Hats: GBB, Guess: G--, Result: Win
Hats: BGG, Guess: B--, Result: Win
Hats: BGB, Guess: -G-, Result: Win
Hats: BBG, Guess: --G, Result: Win
Hats: BBB, Guess: GGG, Result: Lose

Result: 75% chance of winning!

Solution:

Because seven was hungry and 'seven ate nine' (7, 8, 9).

Solution:

Each word has 3 consecutive letters of the alphabet-
couGHIng (GHI)
thiRSTy (RST)
DEFiant (DEF)