Rule out the impossible

Establish the world of the puzzle

Before drawing a grid, identify the objects and the rules connecting them. If three people each choose one activity, are the activities different? Does everyone choose exactly one? Can an activity remain unused? These details determine which eliminations are valid.

A familiar puzzle format can tempt you to import rules that were never stated. Resist that temptation. “Each person has exactly one different activity” creates a one-to-one assignment. Without the word “different,” two people might share an activity, and many standard grid deductions would no longer follow.

The small challenge below states its complete assignment rule. The Nordic setting supplies names and atmosphere only. No knowledge of local customs, geography or language is needed to solve it.

Make each inference inspectable

1. There are three allowed activities. Clue 2 excludes two for Oskar, so Oskar must choose the museum.

2. The one-to-one rule excludes the museum for both Liv and Sanna.

3. Clue 3 excludes the harbour for Sanna. With the museum also excluded, Sanna must choose the forest.

4. The forest and museum are assigned. Liv must choose the harbour.

Notice that clue 1 was not needed to derive the assignment. It is consistent with the result, but redundant given the other conditions. A redundant clue is not necessarily an error: it can help a beginner enter a puzzle or provide a useful cross-check. It should not be mistaken for an essential step in the proof.

Check the completed assignment against every clue, including the redundant one. Liv is not at the museum; Oskar is at neither walking activity; Sanna is not at the harbour. All three activities are used once, so the global assignment rule is satisfied too.

Possible is different from necessary

An assignment is possible if it satisfies all the clues. A fact is necessary if it holds in every satisfying assignment. Finding one valid arrangement proves possibility, not uniqueness. To claim a unique solution, you must rule out every alternative arrangement.

Remove clue 3 from the challenge. Oskar still chooses the museum, but Liv and Sanna can exchange the two walks. Both assignments satisfy the remaining clues. Saying “Liv chooses the harbour” is then possible, but no longer forced.

This small comparison is a powerful diagnostic. When you feel stuck, ask whether you are missing a deduction or whether the clues genuinely permit multiple outcomes. Producing two valid outcomes is a constructive way to demonstrate ambiguity.

Handle “if” with care

A conditional statement has a direction. “If Liv takes the forest walk, Oskar visits the museum” does not by itself say that Oskar's museum visit forces Liv into the forest. Another arrangement could put Oskar at the museum while Liv chooses something else.

To test a conditional, look for its forbidden case: the first part is true and the second part false. That is the combination the statement rules out. Turning the sentence around without justification adds a new rule that the author did not supply.

For larger puzzles, use a table and attach a clue number to each exclusion. Mark temporary assumptions separately from established facts. If an assumption leads to a contradiction, undo its consequences before trying another branch. A tidy record protects the argument from an old guess accidentally becoming a “fact.”

The aim is not to avoid uncertainty at every stage. It is to know which statements are certain, which are provisional and which have been disproved. That distinction makes even a small puzzle a worthwhile exercise in careful explanation.