Answer:
At each stage, a new dot starts at the top, and then goes either clockwise, or counter-clockwise.

Puzzle 2

Each of the following sets of letters can be made into a real word by adding three letters to the beginning, and the same three letters in the same order to the end.

For example, ANGLEM can have ENT added at the start and the end to become ENT + ANGLEM + ENT = ENTANGLEMENT.

ENT + ERTAINM + ENT = ENTERTAINMENT
RED + ISCOVE + RED = REDISCOVERED
ING + ROW + ING = INGROWING
ANT + IOXID + ANT = ANTIOXIDANT
MIC + ROCOS + MIC = MICROCOSMIC

Puzzle 3

A rope swing hangs vertically down so that the end is 12 inches from the ground, and 48 inches from the tree.

If the swing is pulled across so that it touches the tree, it is 20 inches from the ground.

Hint: You might find Pythagoras' theorem very useful [a^{2} + b^{2} = c^{2}].

Answer: 148 inches.

We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled triangle.

The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R - 8 (the difference between 20 inches and 12 inches).

Pythagoras' theorem tells us that:

a^{2} + b^{2} = c^{2}

Where c is the hypotenuse.

This gives us:

48^{2} + (R - 8)^{2} = R^{2}

^{ }^{ } 2304 + (R - 8)(R - 8) = R^{2}

^{ } 2304 + R^{2} - 16R + 64 = R^{2}

^{ }^{ } 2304 - 16R + 64 = 0

^{ }^{ } 16R = 2368

^{ }^{ } R = 148

As required. QED.

Puzzle 4

Using the BrainTracker grid below, how many words can you find? Each word must contain the central P and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?

The BrainBashers safe has a rather unusual control panel. In order to open the safe you have to press every single button once only, in the correct sequence, ending on the button marked E.

Each button clearly states which button to press next, for example, 2U means move up 2 buttons and 3R means move right 3 buttons.

Can you determine which button you must start with?