Random Puzzles 

Workings

Hint
The word begins with the letter A.

Answer
Arm.

Double-Checking
swarm army alarm farm warm

Workings

Hint
What day of the week was the 1^st?

Answer
Saturday.

Reasoning
For a 31-day month, such as March, to have 5 Saturdays and 5 Mondays the 1^st must be a Saturday (and the 31^st a Monday).

You can then work forwards from the 1^st.

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747

Workings

Hint
The eleven-letter word begins with the letter I.

Answer
Investigate.
bake = bike swap = snap opal = oval dyed = deed idle = isle snow = stow lump = limp aces = ages melt = malt spun = stun rant = rent