A counterexample is a case that satisfies the relevant conditions but makes a proposed claim false. It is especially useful when a question asks whether something must always be true.
One case can defeat an all claim
Consider the claim every odd number is prime. The number 9 is odd and equals 3 × 3, so it is not prime. That single example disproves the universal claim.
Listing several odd primes, such as 3, 5 and 7, would not prove the claim. Supporting examples and a counterexample play different logical roles.
Preserve every premise
Suppose all striped counters are blue and some blue counters are large. A proposed conclusion says some striped counters must be large.
Construct a case with one small blue striped counter and one large blue unstriped counter. Both premises hold, but no striped counter is large. The conclusion is therefore not forced.
If your imagined case violated a premise, it would not be a valid counterexample. Always check the original rules first.
Use the smallest clear case
You do not need a complicated imaginary world. A few objects or a short arrangement often suffice. The goal is to show the logical gap with as little extra detail as possible.
For ordering puzzles, try moving an unconstrained item. If the clues remain true while the proposed position changes, that position was not necessary.
Know what the result establishes
Finding a counterexample shows that a must claim fails. It does not necessarily establish the opposite universal claim. Showing that some striped counters need not be large is not the same as showing that striped counters can never be large.
Make it a review habit
When an answer explanation says insufficient information, try building the two allowed cases: one where the proposed conclusion holds and one where it does not. Seeing both makes the uncertainty concrete and helps you resist choosing a conclusion merely because it sounds plausible.