### Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

### Peeling the Apple or the Cone That Lost Its Head

How much peel does an apple have?

### Take Ten Sticks

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

# Robot Camera

##### Age 14 to 16 Challenge Level:

Nanotechnology is the technology of objects whose dimensions are in the range $0.1$ to $100$ nanometre (nm), ie. $0.1\times 10^{-9}$ to $100\times 10^{-9}$ metres. Try these preliminary questions to help you get some idea just how small that is and how it relates to other units of length:

1. An average human hair has a diameter of about 50 microns. How many nanometres is this?
2. Measure the height of a new pack of printer paper. Packs come in reams which contain 500 sheets of paper: estimate the thickness of one piece of paper. What is this in nanometres? What is it in microns?

Do you think that it will be possible in principle to make a robot camera using nanotechnology which could be injected into a person's arteries in order to see if they are becoming blocked? You will need to consider what size a robot would need to be to move along an artery in the blood stream.

Here is some information to get you started:

• the interior diameter of the coronary arteries is about 1-2 mm
• blood contains red and white blood cells and platelets
• red blood cells (erythrocytes) are about 6-8 microns in diameter
• white blood cells (leukocytes) are about 15 microns in diameter
• platelets (thrombocytes) are about 2-3 microns in diameter

Here is an image of blood components taken from http://en.wikipedia.org/wiki/File:Red_White_Blood_cells.jpg