Random Puzzles 

Workings

Hint
The answer involves a square root.

Answer
4.

The middle of each triangle contains the square root of the sum of the three surrounding numbers.

Workings

Hint
Try to rotate them around in your head, but watch out for mirror images.

Answer
A, D, and E.

Workings

Hint
The answer is in the words given.

Answer
Slow.

Reasoning
Take the third letter of the first word
   + the second letter of the second word
      + plus the first letter of the first word
         + plus the fourth letter of the second word.

Double-Checking
3-1- [1234] -2-4
s-f- [fast] -a-t
o-s- [slow] -l-w

Workings

Hint
What's a mathematical way to describe placing a 9 at the beginning?

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 – 36 = 40k – k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore, k = 23,076.

Double-Checking
923,076 = 4 x 230,769.