MathProblem 71 Nine pearls and a scale problem

You have nine pearls, eight are real and one is fake. All the real ones weigh the same and the fake weighs less than the real ones. Using a balance scale twice how can you weed out the fake one?

Solution

8个真的，1个假的，且假的比真的轻。问怎么用两次把假的区分出来。

不能按照 \(4,4,1\) 进行分组，而是应该用 \(3,3,3\) 分组。这样假设 \(fake\) 在最后一组，称了前两组以后知道假的在最后一组，在该组任选两个进行称重即可