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'Four Coloured Lights' printed from http://nrich.maths.org/

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light machine
Imagine a machine with four coloured lights and a keypad for entering numbers.

Each light responds to a different rule. When a number is typed in, lights go on if their rule is satisfied. If the number satisfies more than one rule, then more than one colour will light up.

Your challenge is to find the smallest possible number which will make all four colours light up.

Here are some data which have been collected about the responses from the machine. Try to make sense of the information and figure out the rules used by the machine.

A second machine works in the same way but according to a different set of rules. Here are the data from the second machine.

Send us your solution for a number which will turn on all the lights, with an explanation of how you arrived at your answer.