Random Puzzles 

Workings

Hint
There are 60 seconds in a minute, and 60 minutes in an hour.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 60 x 24 x 365 = 525,600 minutes in a (non-leap) year.

Workings

Hint
Start by filling the 7 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  7    fill B
3  4    fill A from B
0  4    empty A
3  1    fill A from B
0  1    empty A
1  0    fill A from B
1  7    fill B
3  5    fill A from B

This leaves 5 gallons in container B after 8 steps.

Workings

Hint
How many statements would be true if the culprit was Alex?

Answer
Emery committed the crime.

Reasoning
If we assume that Alex was the culprit, we can see that there would be 6 true statements, but we know there were exactly 5 true statements, so it can't be Alex.

We can repeat this will all five suspects and quickly see that only Emery being the culprit would result in exactly 5 statements being true.

Workings

Hint
How many rats can one cat catch in 5 minutes?

Answer
5.

  5 cats can catch 5 rats in 5 minutes.

So

  1 cat can catch 1 rat in 5 minutes.

  1 cat can catch 2 rats in 10 minutes.

  1 cat can catch 20 rats in 100 minutes.

Therefore

  5 cats can catch 100 rats in 100 minutes.