Puzzles — Fundamental Concepts

Fundamental Concepts

Start by listing the objects and their possible positions or attributes. Translate fixed positions first, then adjacency blocks, relative-order clues and exclusions. A before B allows a gap unless immediately is stated. At least two allows more than two. Interpret either-or according to the wording rather than silently assuming that exactly one alternative is intended.

In the original four-day puzzle, A is before C, B immediately follows D, and C is not Thursday. Test the D–B block on Monday–Tuesday, Tuesday–Wednesday and Wednesday–Thursday. The first two cases force C onto Thursday, so they fail. The last leaves A Monday and C Tuesday, producing A, C, D, B. This shows how a strong adjacency clue reduces the search and an exclusion supplies uniqueness.

Keep temporary branches separate. A placement valid within one case is not automatically true in every case. If two complete arrangements survive, compare the requested statement across both. One valid witness establishes could be true; every surviving arrangement must support must be true. A valid counterexample defeats a necessity claim.

For seating, mark the direction people face before interpreting left and right. A south-facing person's left points east on a conventional map. In circular arrangements, fixing a reference removes irrelevant rotations, but reflection can still change left-right relationships. Recheck every original clue against a completed arrangement before using it as evidence.