### 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?

### Arithmagons

Can you find the values at the vertices when you know the values on the edges?

### Babylon Numbers

Can you make a hypothesis to explain these ancient numbers?

# Reaction Timer

##### Age 11 to 14Challenge Level

In this problem, you will meet two different ways to test your reactions.

This reaction timer will enable you to collect data on the time it takes you to respond to an image on your computer.

Open animation in new window

Note: You can copy/paste the results table into a spreadsheet

Here is a second experiment you can use to test your reactions.
Ask a friend to hold a ruler by the end, above your hand. Open your hand below the ruler and be ready to catch it. Your friend will drop the ruler without saying when they're going to let go. Catch the ruler as fast as you can after it's been dropped.
The pictures below show this experiment being carried out:

Record the level (in centimetres) at which you caught the ruler, and repeat the experiment several times. If you have quick reactions, the ruler will not have travelled far when you catch it.

Taking only one measurement in either of these experiments will not give you a reliable, accurate measure of speeds of reaction that could be used to rank a group of people.

Decide how many measurements you will take, and what you will do with them to provide an accurate measure of reaction speeds. Make sure you can justify your decisions.

#### Here are some questions you might like to consider:

• I think I respond more quickly with my right hand than with my left - are you the same?
• Do your reactions vary depending on the time of day or the sort of thing you are being asked to react to?
• Do your reactions improve with training/practice?
• Do boys react more quickly than girls?
• Do young people react more quickly than older people?
• What else do you think affects people's reaction times?
• Are both experiments testing the same ability? If you perform both experiments with a group of people and rank them in order, will the rankings be the same for both experiments?
• Can you think of other experiments you could do to test your reactions?
Test any hypotheses you come up with.

You may also wish to explore how accurately you can estimate time.