Random Puzzles 

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
There are fewer than 20 squares.

Answer
18 squares.

In the solution below, you can see 6 squares in the middle, with another 12 squares around the outside.

Workings

Hint
The first letters of the names are: G, R, E, P, M, E, A, A.

Answer
gl    = Gail
rs    = Rose or Iris
dth   = Edith
ptsy  = Patsy
mxn   = Maxine
dwn   = Edwina or Dawn
gth   = Agatha
dry   = Audrey

Workings

Hint
Start by looking at the 6 and 4 on the top row.

Answer