Random Puzzles 

Workings

Hint
Think about the 40%, and how many buses that represents.

Answer
72 buses.

Reasoning
The garage is currently full, with 12 more buses outside.

If we increase the garage space by 40%, there will be enough space to house those 12 buses, plus 12 more in the future, a total of 24 buses.

This means that 40% of the current garage capacity is 24 buses.

Therefore, 10% of the current garage capacity is 6 buses.

Therefore, 100% of the current garage capacity is 60 buses.

So, the current garage holds 60 buses, and there are 12 more outside.

Therefore, we have a total of 72 buses.

Double-Checking
They currently have 72 buses, 12 of which are outside, so 60 are inside.

Increasing the garage space of 60 buses by 40% will give room for 60 x 1.4 = 84 buses.

Which is the 72 they currently own, with space for 12 more buses in the future.

This confirms the answer.

Workings

Hint
You can only go up, or right.

Answer
6.

With U = Up, and R = Right, you can move in the following ways:
UURR
URUR
URRU
RUUR
RURU
RRUU

Workings

Hint
Remember that each of them told the truth in one of their statements, but lied in the other.

Answer
Billie robbed the bank.

Reasoning
We know that each of them told the truth in one of the statements and lied in the other.

So according to Ashley, as one of the statements is false, it must have been either Drew or Billie.

If it was Drew, then Billie's statements would both be true, which isn't allowed.

Therefore, it was Billie, which agrees with Casey and Drew's statements.

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.