You have nine identical-looking balls. Eight weigh the same. One is heavier.
You have a balance scale and may use it only twice.
How do you find the heavy ball for sure?
Answer
Split into three groups of three. Weigh two groups. Take the heavy group (or the leftover if equal). Repeat.
A balance gives three outcomes each time, so two weighings can distinguish 9 cases. Grouping by threes uses that ternary split cleanly.
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The general version of this puzzle
Nine balls in two weighings is a counting result, not a lucky guess: a balance returns one of three outcomes, so two uses separate nine cases exactly. The general form has a name:
