### Where Can We Visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

### The Mathemagician's Seven Spells

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

### Folding, Cutting and Punching

Exploring and predicting folding, cutting and punching holes and making spirals.

# White Box

##### Stage: 2, 3, 4 and 5 Challenge Level:

The White Box contains a number of filled triangles.

Your challenge is to find the locations of those filled triangles in the grid.

You can fire rays into The White Box and observe where the rays exit using the Experiment Window.

Some rays will pass straight through the Box but some will be deflected by the filled triangles.

You can use the Hypothesis Window to test your ideas. Clicking on a triangle once marks the triangle as empty, clicking again fills it.

FULL SCREEN VERSION

This text is usually replaced by the Flash movie.

NOTES AND BACKGROUND

Anyone attempting to understand anything about the nature of atoms and molecules has to try to come to terms with their almost inconceivably tiny nature. A single hair is about the same width as a million atoms; a glass of water contains about 10 000 000 000 000 000 000 000 000 molecules. The minute size means that they're beyond the range of even the most powerful microscope, so to gain understanding about the ways atoms are arranged within crystals and molecules, scientists need to use indirect methods.

One method involves firing rays of sufficient energy to break bits off the molecules. These particles will of course be smaller still, but they may be easier to recognise. The experimenter can then use the pieces like a jigsaw to explore how they fitted together in the original molecule.

A less destructive process involves not breaking up the structure, but deducing its arrangement by observing the areas where rays fired into it emerge. Some rays pass straight through, while others are deflected by atoms within the structure. The White Box interactivity models this process and makes an intriguing challenge as well.