Random Puzzles 

Workings

Hint
Try removing some letters.

Answer
Carrot.

Reasoning
Each of the other words remains a real word if you remove the first and last letter:
s-event-y b-raw-l c-love-r p-rope-r c-arro-t * s-win-g e-merge-d c-raft-y t-rave-l s-acre-d s-ton-e p-lung-e

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
Can you see 1, 2, 3, …?

Answer
46.

Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1  1   (1 x 1 = 1,  reversed is 1)
2  4   (2 x 2 = 4,  reversed is 4)
3  9   (3 x 3 = 9,  reversed is 9)
4  61  (4 x 4 = 16, reversed is 61)
5  52  (5 x 5 = 25, reversed is 52)
6  63  (6 x 6 = 36, reversed is 63)
7  94  (7 x 7 = 49, reversed is 94)
   so we require:
8  46  (8 x 8 = 64, reversed is 46)

Workings

Hint
The second word is CORD.

Answer
COLD, CORD, WORD, WARD, WARM

or

COLD, CORD, WORD, WORM, WARM

or

COLD, CORD, CARD, WARD, WARM.