Editorial for COCI '06 Contest 4 #3 Prsteni

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The number of times the $i^{th}$ $i^{t h}$ ring turns depends only on its radius and the radius of the first ring. The sought ratio is $R_i / R_1$ $R_{i} / R_{1}$ . Reducing the fractions can be done by dividing the numerator and denominator by their greatest common divisor, given by the recursive formula:

$\displaystyle \gcd(a,b) = \begin{cases}a & \text{when }b=0 \\ \gcd(b, a \bmod b) & \text{when }b \ne 0\end{cases}$ $gcd (a, b) = {\begin{cases} a & when b = 0 \\ gcd (b, a mod b) & when b \neq 0 \end{cases}$

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