Random Puzzles 

Workings

Hint
The cube root of the given number is a good starting point.

Answer
71, 73, 79.

Reasoning
The cube root of 409,457 is around 74.

The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.

Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.

Workings

Hint
Think of the whole alphabet, and not just the vowels (AEIOU).

Answer
8,300.

Each letter of the country is worth 100 miles based on its position in the alphabet.

Therefore, Germany = 7 + 5 + 18 + 13 + 1 + 14 + 25 = 83 x 100 miles.

Workings

Hints
Try: pale + tone, veil + june, peer + date.

Answers
pale + tone = antelope
veil + june = juvenile
peer + date = repeated, departee
snob + wall = snowball
time + seat = estimate, meatiest, teatimes

Workings

Hint
What day of the week was the 1^st?

Answer
Saturday.

Reasoning
For a 31-day month, such as March, to have 5 Saturdays and 5 Mondays the 1^st must be a Saturday (and the 31^st a Monday).

You can then work forwards from the 1^st.