### 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?

# Charlie's Delightful Machine

##### Age 11 to 16Challenge Level

You may wish to look at Shifting Times Tables before trying this problem.

Can you work out how to switch the lights on?

Charlie's Delightful Machine has four coloured lights. Each light is controlled by a rule.
If you choose a number that satisfies the rule, the light will go on.
Some numbers may turn on more than one light!

Start by exploring Level 1. Type in some numbers and see which lights you can switch on.
To start again with a new set of rules, click the Level 1 button.

Can you develop a strategy to work out the rules controlling each light?

Once you have a strategy, challenge yourself to find some four-digit numbers that turn on each light.

Once you are confident that you can work out the rules for Level 1 lights, have a go at A Little Light Thinking, where you can explore how to turn on several lights at once.

You may also wish to explore the Level 2 and 3 lights (which use a different type of sequence) in the same way.

You may also be interested in the other problems in our Cracking Codes Feature.