Mathematical Puzzles — Prelims Strategy

Prelims Strategy

Name the unknowns and their units before manipulating numbers. For digits, state the permitted ranges and distinguish the original from the reversed number. For ages, label present and future values explicitly. For transfers, draw an initial-state row and a separate row for each alternative; check that the total is conserved in every row.

Translate comparative wording accurately. Twenty-seven smaller fixes a subtraction direction. Twice as many gives a ratio in the specified state. Least greater than one hundred combines an ordering condition with arithmetic constraints. Keep these clauses visible so that a partial solution is not mistaken for the final answer.

Use the answer options efficiently after building the model. Substitution may reject candidates faster than a full symbolic derivation, but each condition still needs checking. For remainder problems, identify the repeating interval when useful and then apply the size bound. For sequences, verify the stated pattern across every transition; do not switch rules to accommodate a preferred option. Finish with a quick check of sign, integrality and the requested time or state.