Problem solving
Turn conditions into a clear model, then test each conclusion against every condition.
A reliable solving method
- Identify the goal. Decide exactly what must be found: a value, order, category, or conclusion.
- Record the conditions. Translate each sentence into a short equation, table, diagram, or true/false rule.
- Apply constraints together. Eliminate a candidate as soon as it violates one condition; do not rely on a single clue.
- Check the result. Substitute the answer back into every condition and make sure the question asked for that quantity.
Worked example: intersecting conditions
A number is between 20 and 50, is divisible by 6, and leaves remainder 2 when divided by 5. Find it.
Solution: Multiples of 6 in the interval are 24, 30, 36, 42, 48. Only 42 leaves remainder 2 on division by 5, so the number is 42.
Practice · original questions
- A number from 20 to 45 is divisible by both 3 and 4. What is the largest possible number?
- Every lamp is either red or green, never both. No green lamp is metal. A lamp is metal. What follows?
- A code uses the rule “double the number, then add 3.” What code value corresponds to 8?
Show answers and reasoning
- 36. Common multiples of 3 and 4 are multiples of 12; 36 is the largest in the range.
- The lamp is red. It cannot be green, and every lamp is exactly one of the two colours.
- 19. Apply the rule in order: 8 × 2 + 3 = 19.