Bunuel
A regional courier makes exactly seven deliveries each day, to Delivery Hubs North, East, West, Central, Ridge, Harbor, and Valley. The hub receiving the shipment with the highest priority is visited first, and each subsequent delivery is scheduled to the hub with the shortest travel time from the one most recently served. The table below shows the travel times between these delivery hubs, in minutes.
| Hub | North | East | West | Central | Ridge | Harbor | Valley |
|---|
| North | 0 | 6 | 3 | 4 | 8 | 5 | 7 |
| East | 6 | 0 | 5 | 3 | 9 | 4 | 6 |
| West | 3 | 5 | 0 | 2 | 10 | 6 | 4 |
| Central | 4 | 3 | 2 | 0 | 5 | 7 | 6 |
| Ridge | 8 | 9 | 10 | 5 | 0 | 8 | 7 |
| Harbor | 5 | 4 | 6 | 7 | 8 | 0 | 3 |
| Valley | 7 | 6 | 4 | 6 | 7 | 3 | 0 |
On Thursday, the highest-priority shipment is to Hub Central, and the first delivery is therefore made to Hub Central.
For each of the following sequences of hubs, select
Yes if the courier will visit the three hubs in the given order. Otherwise, select
No.
The courier begins at the hub with the highest-priority shipment, which is
Hub Central. After each delivery, the courier selects the next hub that has the
shortest travel time from the most recently visited hub among those not yet served.
From Hub Central, the travel times are:
West 2, East 3, North 4, Ridge 5, Valley 6, Harbor 7.
The nearest is West, so the second stop is
Hub West.
From Hub West, the travel times to unvisited hubs are:
Central (already visited), East 5, North 3, Ridge 10, Valley 4, Harbor 6.
The nearest is North (3), so the third stop is
Hub North.
From Hub North, the travel times to unvisited hubs are:
East 6, Ridge 8, Harbor 5, Valley 7.
The nearest is Harbor (5), so the fourth stop is
Hub Harbor.
From Hub Harbor, the remaining unvisited hubs are East, Ridge, and Valley.
Travel times: East 4, Ridge 8, Valley 3.
The nearest is Valley (3), so the fifth stop is
Hub Valley.
From Hub Valley, the remaining unvisited hubs are East and Ridge.
Travel times: East 6, Ridge 7.
The nearest is East (6), so the sixth stop is
Hub East.
The final unvisited hub is Ridge, so the last stop is
Hub Ridge.
The full route is therefore:
Central → West → North → Harbor → Valley → East → Ridge
• Hub Central then Hub West then Hub HarborCentral is followed by West, and West is followed by North, not Harbor. Hence this sequence does not occur.
Answer:
No• Hub Ridge then Hub East then Hub ValleyRidge is the last stop, and East is visited before Ridge. Hence Ridge cannot precede East or Valley.
Answer:
No• Hub North then Hub Harbor then Hub ValleyNorth is followed by Harbor, and Harbor is followed by Valley in the route. Hence this sequence occurs.
Answer:
YesI29-219