Random Puzzles 

Workings

Hint
You can only go up, or right.

Answer
6.

With U = Up, and R = Right, you can move in the following ways:
UURR
URUR
URRU
RUUR
RURU
RRUU

Workings

Hint
Calendar.

Answer
Dragon.

From the Chinese calendar in reverse order.

Workings

Hint
This is a tricky question related to number bases.

Answer
200.

Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32  = 3 x 10^1 + 2 x 10^0          = 3 x 10 + 2         = 32
Base 9 : 35  = 3 x 9^1  + 5 x 9^0           = 3 x 9 + 5          = 32
Base 8 : 40  = 4 x 8^1  + 0 x 8^0           = 4 x 8 + 0          = 32
Base 7 : 44  = 4 x 7^1  + 4 x 7^0           = 4 x 7 + 4          = 32
Base 6 : 52  = 5 x 6^1  + 2 x 6^0           = 5 x 6 + 2          = 32
Base 5 : 112 = 1 x 5^2  + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2  + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0     = 32

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.