Random Puzzles 

Workings

Hint
How much is each vowel (AEIOU) worth?

Answer
29,000 miles.

Reasoning
Each vowel (AEIOU) is worth 4,000 miles and each consonant is worth 5,000 miles.

Double-Checking
Sydney has 1 vowel (E = 1 x 4,000) and 5 consonants (SYDNY = 5 x 5,000) = 29 thousand miles.

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy …

We have:

   10^1/10 or 2^1/3

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1/10)³⁰ or (2^1/3)³⁰

   10^{1/10 x 30} or 2^{1/3 x 30}

   10³ or 2¹⁰

   1000 or 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
Work out the total number of legs.

Answer
23 children (46 legs).

With 230 ants (1380 legs), 3 puppies (12 legs), and 1 teacher (2 legs).

If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies:
 P x 4 =  4P

Children:
 (P + 20) x 2 =  2P + 40

Ants:
 10 x (P + 20) x 6 = 60P + 1200

Teacher: 2

A total of 66P + 1242

Giving:

 66P + 1242 = 1440

 66P        = 198

   P        = 3

So there were 3 puppies, hence 23 children.

Workings

Hint
Remember that you can't have three White or Blue squares together in a row or column.

Answer