From conditions to a solution
A route task asks you to connect places while respecting its rules. A written problem asks you to separate given facts from what must be established. In both, an attractive answer still needs checking against the conditions.
Different aspects of thinking
Logical validity, the usefulness of a new idea and speed under a specified difficulty are different criteria. One fast result cannot summarize all of them. Some tasks have one valid answer; others permit several solutions worth comparing.
Plan, solve and check
Try the travelling salesperson task: first produce a route satisfying the rules, then compare its length with another valid route. Away from the trainer, write the known facts, goal and constraints of a problem. Explain each step and check the final result.
Plan completion before the courier arrives
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Your result
Step-by-step worked example
What to prepare
Write down the conditions. Work begins at 15:30. Durations are supplied for this exercise; check both dependencies and the deadline.
Task sample
What to do, step by step
State the goal: packed documents ready by 16:00. Record which action depends on another.
Arrange the three actions in a valid order, without signing before printing or packing before signing.
Calculate each start and finish time from 15:30.
Compare readiness with the deadline and explain whether every condition is satisfied before judging convenience.
How to check your result
Print 15:30–15:40, sign 15:40–15:45, pack 15:45–15:50. Documents are ready ten minutes before arrival. Check order and timing: a correct final time does not make a dependency-breaking plan valid.
Your next attempt
Change one duration or the deadline and recalculate. Check feasibility first, then compare valid options.
Examples in everyday tasks
Plan tasks with dependencies
Documents must be printed, signed and handed to a courier before 4 p.m. Signing requires printing first, and the courier visits once. Write the constraints and arrange the actions. Thinking here connects conditions to the goal and checks feasibility, rather than merely listing things to do.
Check what an announcement implies
A website says all evening-course students receive a recording. A friend received it. Does that establish evening-course enrollment? No: other groups might also receive access. The example checks what follows from the statement without inventing a restriction it never supplied.
Choose a feasible route
Several city routes could cover three errands. First exclude routes that reach a shop after closing. Then compare valid routes by a chosen criterion, such as time or distance. The decision combines checking constraints with selecting among acceptable options; the shortest route may fail the task.
