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# Charlie's Delightful Machine

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Age 11 to 16

Challenge 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.*

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.