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'Colour Wheels' printed from http://nrich.maths.org/

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Imagine a wheel with different coloured markings - red, green and blue painted on it at regular intervals.
As the wheel goes round, a trail is painted on the ground.
RGBRGBRGBRGBRGBRGB ... ...

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Satisfy yourself that you can predict where the blues will appear.
How about the red and green marks?

Can you predict the colour of the 18th? 19th? 31st? 59th? 299th? 3311th? 96 312th?
How did you work it out?

Now consider the wheels that produce:

BBYGBBYGBBYG ... ...
BYBRBYBRBYBRBYBR ... ...
RRRBBYRRRBBYRRRBBYRRRBBYRRRBBY ... ...
RRBRRRRBRRRRBRRRRBRRRRBRR ... ...

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What will the 24th colour be in each case? The 49th colour? The 100th?
How did you work it out?

You could continue this investigation by asking yourself some "what if ...?" questions:

A wheel has six markings. Where would red be painted on it so that the 100th mark made is red?

What other wheels (with more/fewer markings) would give you a red in the 100th position?