Brain Teasers

Match stick tricks

Here is one serious and one not-so-serious trick with matches. Try them out, but be careful with matches!
1. Remove six matches from the set below, leaving ten.
2. Change the position of two matches to reduce the number of squares in the figure from five to four. All matches must be part of a square so no "loose ends" are left.

Square pegs and round pegs
You may have heard the phrase "putting a square peg in a round hole". This means doing something that does not quite fit or match since round pegs are best put in round holes, and square pegs in square ones! Now the question is, does a round peg fit better in a square hole or does a square peg fit better in a round hole?
Hint: Imagine that in both cases, the size of the peg and hole are the same. So, for instance, the diameter of the round peg is the same as the side of the square hole, so the mismatch is in the shape. The question then reduces to finding out how much gap is "left over" between the hole and the peg. This amounts to asking what is the relative difference in the left-over area between the peg and the hole, as seen in the figure.
Adapted from "Mathematical Circus" by Martin Gardner