Random Puzzles 

Workings

Hint
Remember that you have the same number of each coin.

Answer
134 of each coin.

Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.

And 2p + 5p + 10p + 20p = 37p.

There are 134 lots of 37p in £49.58.

Double-Checking
134 x 37 = 4958.

Workings

Hint
All of the words are three letters long.

Answers
First set:
bot = small robot bit = small part but = on the contrary bat = nocturnal mammal bet = wager
Second set:
hit = struck het = heated (archaic British) hut = straw dwelling hat = a head warmer hot = not cold

Workings

Hint
Try starting with the cube root of the number.

Answer
195 x 197 x 199.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.

Let's try dividing by the closest odd number to 196.99:

   7644585 ÷ 197 = 38805

We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.

Trying either 195 or 199 gives the answer.

Double-Checking
   195 x 197 x 199 = 7,644,585

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.

Workings

Hint
Look at the first letters.

Answer
November.

This is the next month in alphabetical order:

April, August, December, February, January, July, June, March, May, November, October, September.