Random Puzzles 

Workings

Hint
What could we do with the digits?

Answer
If the sum of the digits is divisible by nine, so is the number.

Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.

For example, is 486451464 divisible by 9?

Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.

Is 42 divisible by 9? Not sure, you can then do:

4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.

Workings

Hint
Look at the vowels (AEIOU).

Answer
2.

Consonants are worth 2 and vowels (AEIOU) are worth –1.

Workings

Hint
The country spans more than one word.

Answer
Guinea.

During the recent BrainBashers aquatic contest, the walrus struggled to finish, the sea lion finished second, and the penGUIN EAsily won!

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 and 7 x 2 = 14.

6 x 8 = 48 and 4 x 8 = 32.

8 x 8 = 64 and 6 x 4 = 24.