Puzzle 1

Burning rope

If you light both ends of one rope, it will burn in exactly a 1/2 hour. Thus, burn one rope from both ends and the other rope from only one end. Once the one rope (which is burning from both ends) finally burns out (and you know a 1/2 hour has elapsed), you also know that the other rope (which is buring from only one end) has exactly 1/2 hour left to burn. Since you only want 45 minutes, light the second end of the rope. This remaining piece will burn in 15 minutes. Thus, totaling 45 minutes.

Puzzle 2

A quick test of intelligence

There are six F's in the sentence.
A person of average intelligence finds three of them.
If you spotted four, you're above average.
If you got five, you can turn your nose at most anybody.
If you caught six, you are a genius.
There is no catch.
Many people forget the "OF"'s.
The human brain tends to see them as V's and not F's.
Pretty weird, huh?