Random Puzzles 

Workings

Hint
Think of an alternative alphabet.

Answer
N.

From epsiloN, last letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu.

Workings

Hint
There are two sequences merged.

Answer
10.

Reasoning
There are two sequences mixed together.

0 1 2 3 4 5

and

0 2 4 6 8 ?

Workings

Hint
Start by filling the 9 gallon container, and then use that to fill the 4 gallon container.

Answer
Here are the contents of the containers after each stage:
A   B
9   0      fill A
5   4      fill B from A
5   0      empty B
1   4      fill B from A
1   0      empty B
0   1      fill B from A
9   1      fill A
6   4      fill B from A
6   0      empty B

This leaves 6 gallons in container A.

Workings

Hint
The word DECEMBER appears 19 times.

Answer
The word DECEMBER appears 19 times.