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
The answer is a whole number less than 10.

Answer
3.

Reasoning
We can multiply throughout by 12,
    X     X     X     X
    -  -  -  +  -  =  -
    X     2     4     12

to give:

   12 − 6X + 3X = X

        12 − 3X = X

             12 = 4X

              3 = X

As required.

Double-Checking
    3     3     3     3
    -  -  -  +  -  =  -
    3     2     4     12

    1 − 1.5 + 0.75 = 0.25

              0.25 = 0.25, which confirms that 3 is correct.

Workings

Hint
The missing word ends with the letter D.

Answer
The missing word is BREAD.

Workings

Hint
Try removing the Y from ENERGY.

Answers
energy    -y = green oregano   -o = orange clearest  -e = scarlet weight    -g = white outlive   -u = violet embark    -k = amber calmer    -l = cream or -r = camel solemn    -s = lemon voiding   -v = indigo archery   -a = cherry