The nine coins
One coin is heavier. Two weighings, many possible strategies.
Find the heavier of nine coins using a balance at most twice. The other eight have equal weight.
What you will practise: Rule out possibilities using a comparison.
Think it through together
One person proposes a strategy; the other asks “why?” and looks for a case where it fails. Then swap roles. No names or speed competition needed.
Before viewing the explanation: what do we know, what are we assuming, and how would we check the result?