Random Puzzles 

Workings

Hint
The answer involves multiplication (for example, 9 x 8 = 72).

Answer
468.

Reasoning
If we split each line in the following way:

98 68 88
72 48 64
14 32 24

Each new line is generated by multiplying the digits two at a time and writing the result below.

For example, 9 x 8 = 72, so 72 appears directly below 98.

And 7 x 2 = 14, so 14 appears directly below 72.

Double-Checking
9 x 8 = 72, 7 x 2 = 14, 1 x 4 = 4.

6 x 8 = 48, 4 x 8 = 32, 3 x 2 = 6.

8 x 8 = 64, 6 x 4 = 24, 2 x 4 = 8.

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
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
Does the answer change = NO.

Answer