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Sunday Afternoon Maths XXI

 Posted on 2014-07-20 

Wool circles

\(n\) people stand in a circle. The first person takes a ball of wool, holds the end and passes the ball to his right, missing a people. Each person who receives the wool holds it and passes the ball on to their right, missing \(a\) people. Once the ball returns to the first person, a different coloured ball of wool is given to someone who isn't holding anything and the process is repeated. This is done until everyone is holding wool. For example, if \(n=10\) and \(a=3\):
In this example, two different coloured balls of wool are needed.
In terms of \(n\) and \(a\), how many different coloured balls of wool are needed?

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Tags: numbers

Sum equals product

\(3\) and \(1.5\) are a special pair of numbers, as \(3+1.5=4.5\) and \(3\times 1.5=4.5\) so \(3+1.5=3\times 1.5\).
Given a number \(a\), can you find a number \(b\) such that \(a+b=a\times b\)?

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Tags: numbers
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