Thinking Cap

Puzzle 13 Doing more with less

The first two diagrams show how four dots may be contained and separated by four squares. The third diagram shows nine dots; can you contain and separate each of the nine dots by using only three squares?

To be clear, each of the nine dots must be completely enclosed by the lines you draw. The areas enclosing the dots do not all have to be of the same size. The lines you draw must describe squares, and only three squares. Therefore you will draw a total of 12 lines.

HINT

As enclosing each dot in its own square, as in the first diagrams with four dots, obviously does not provide a solution, you need to find a more efficient and elegant way of deploying your three squares.

Puzzle 15 Fluctuating weight

If you stand on accurate scales, the display shows your weight oscillating no matter how still you stand. Why?

HINT

What is moving when you are still?

Puzzle 16 True or false

If you travel down a mine shaft a few miles deep (such as the TauTona Mine in South Africa, a gold mine which is 2.4 miles deep) you will weigh slightly less than you did on the surface of the earth.