The Twelve Matchsticks

With 12 matches you can easily create a shape with area 9 and a shape with area 5, as shown on the picture below. Can you rearrange the 12 matchsticks, so that they encompass an area of 4?

Remark: You should have only one resulting shape and no matches should be unused.

First, create a Pythagorean triangle with sides 3, 4, 5, and area 6. Then simply flip its right angle inwards, so that the area decreases by 2.

Twiddled Bolts

Two identical bolts are placed together so their grooves intermesh. If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so it does not rotate and twiddling them in the direction shown below, will the heads:

(a) move inward
(b) move outward, or
(c) remain the same distance from each other?

One of the bolts will be screwing itself, and the other one will be unscrewing itself. This will happen at the same pace and the bolts will remain the same distance from each other. Thus the answer is (c).

The Magnetic Rod

You are in a room with nothing else but two indistinguishable iron rods. You know that one of them is magnetized, how can you figure out which one?

Touch the middle of the first rod with the end of the second rod. If the two rods get attracted to each other, then the second one is the magnet. If not, then the first one is the magnet.