ITPEC IP October 2024 Question 72
A person wishes to start at point X, pass through all of points A, B, and C, and arrive at point Y. When the routes and the required times between points are as shown in the figure and the table, what is the shortest time in minutes from point X to point Y? Here, the points A, B, and C may be passed through in any order.
Explanation
130 minutes — list the visiting orders of A, B and C, keep only those whose last point connects to Y, and take the smallest total.
Only B and C have a route to Y (60 minutes each), so the last point visited must be B or C:
Orders ending at A (X → B → C → A and X → C → B → A) would have to go back through B or C to reach Y and take at least 160 minutes. The minimum is X → A → C → B → Y.
Answer (b)
Why not others:
- •(a) 110 — the route X → A → C → Y, 20 + 30 + 60, which skips B
- •(c) 140 — the order X → A → B → C → Y, which uses the slow 40-minute A–B link
- •(d) 150 — the order X → B → A → C → Y, again using the A–B link
Key rule: With only a few mandatory points, enumerate every visiting order, discard orders that use a missing link, and compare the totals; check that the winning route really visits every required point.
Basic Theory · AI-written, may contain errors
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