Solution

Since, 

$666$ is eventual winner, the balls numbered $4$ and $6$ are lighter and the winning number would be combination of 4s and 6s.

The number of potential winners is given by the number of ways 3 digit numbers can be formed using 4 and 6, i.e. $2 \times 2\times 2=8.$ [ using extended $mn$ rule ].

Answer

8

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