Linear Arrangements — Prelims Strategy

Prelims Strategy

Number the slots before placing people and mark the facing direction. Translate “immediate left” as adjacency with orientation, while “second to the left” means a two-position offset. Keep “somewhere left” separate because it does not fix the distance. Check whether the stem states that everyone faces the same direction.

Place the strongest constraints first: an end position, a fixed gap or a linked block. Maintain separate branches where a clue permits alternatives rather than silently choosing one. After each placement, test the negative clues as well as the positive ones. A diagram that satisfies the most memorable clue can still violate a non-adjacency condition.

Before solving the whole layout, read the question. A necessary relation may be common to several valid arrangements, so uniqueness of the full sequence may not be required. Conversely, one valid example proves possibility rather than necessity. Recheck the requested person's perspective and count positions, not the number of people between them, when interpreting an ordinal offset.