Formalize a Minimum-Trip Transport Puzzle with Horses and Ladders
CiscoSoftware Engineer · Technical ScreenLast updated
Model a horses-and-ladders transport puzzle by clarifying legal moves, tracking resource state, and proving a minimum-trip plan is optimal.
A transport puzzle asks you to move X horses from one side to the other using Y ladders, with the fewest trips back and forth. The movement and capacity rules have not yet been given.
Explain which rules you must establish before a minimum trip count is meaningful, how you would represent the resulting puzzle, and how you would prove that a proposed plan uses the fewest legal trips. This is a conceptual reasoning exercise, not a request for a numerical answer under invented rules.
Constraints and Clarifications
X and Y denote the numbers of horses and ladders; no particular values are supplied. The two sides are distinct locations. Clarify the role of a ladder rather than assuming that it is a boat, a bridge, or a passenger-carrying device.
Clarifying Questions
- What exactly does a ladder enable, how many horses can move at once, and can ladders themselves move between sides?
- Where do the ladders start, and who or what is required to operate or return them?
- Are there restrictions on which horses can move together, or on horses left behind on either side?
- Does one "trip" mean a one-way crossing, a complete outward-and-return round trip, or a simultaneous movement of several groups?
- Must ladders end on a specified side, and does every horse need to finish on the destination side at the same time?
Hints
Hint 1
Check a plan against every transition rule: A small arithmetic count is not a valid solution if one of its crossings cannot occur from the state reached by the previous crossing. Track where every relevant resource is after each move.
Follow-up questions
- How would the search change if one-way trips had different costs instead of each counting equally?
- When could horses be represented only by a count, and when would their individual identities matter?
- How could a valid plan still fail to prove that the number of trips is minimal?
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