River Crossing Puzzle Solution
This is a classic river crossing puzzle. The goal is to move a boatman, a dog, a cat, and a container of milk to the other side of a river. The boat can only carry the boatman and one other item per trip. The key constraints are that the cat cannot be left alone with the dog, nor alone with the milk, on either river bank.
Constraints Analysis
- Boatman must operate the boat.
- Boat capacity: Boatman + 1 item.
- Constraint 1: Cat (C) and Dog (D) cannot be left alone together.
- Constraint 2: Cat (C) and Milk (M) cannot be left alone together.
Step-by-Step Solution
We denote the starting bank as Bank 1 and the destination bank as Bank 2. The items are Boatman (B), Dog (D), Cat (C), and Milk (M).
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Trip 1: B takes C across (Bank 1 → Bank 2).
- Status: Bank 1 = {D, M} (Safe) | Bank 2 = {B, C}
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Trip 2: B returns alone (Bank 2 → Bank 1).
- Status: Bank 1 = {B, D, M} | Bank 2 = {C} (Safe)
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Trip 3: B takes D across (Bank 1 → Bank 2).
- Status: Bank 1 = {M} (Safe) | Bank 2 = {B, C, D} (Safe as B is present)
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Trip 4: B returns with C (Bank 2 → Bank 1). This step is crucial to prevent C and D being left alone.
- Status: Bank 1 = {B, C, M} (Safe as B is present) | Bank 2 = {D} (Safe)
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Trip 5: B takes M across (Bank 1 → Bank 2).
- Status: Bank 1 = {C} (Safe) | Bank 2 = {B, D, M} (Safe)
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Trip 6: B returns alone (Bank 2 → Bank 1).
- Status: Bank 1 = {B, C} | Bank 2 = {D, M} (Safe)
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Trip 7: B takes C across (Bank 1 → Bank 2).
- Status: Bank 1 = {} | Bank 2 = {B, D, M, C} (All items successfully transported)
Conclusion
Following these steps ensures all constraints are met at every stage. The minimum number of crossings required is 7.
Important Questions from Puzzle (Notes)
- Seven boxes S, F, G, H, T and U are kept one over the other but not necessarily in the same order. Only two boxes are kept below S. Only one box is kept above U. Only one box is kept between U and B. G is kept immediately above F. T is kept at some place below H.
How many boxes are kept between H and G? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. H is kept immediately above E. T is kept immediately above U. Only F is kept above S. Only two boxes are kept above H. T is not kept at third position from the bottom.
How many boxes are kept between G and F? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F? Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only four boxes are kept between H and E. Only S is kept above H. Only two boxes are kept between F and U. T is kept immediately above G. U is not kept immediately above T. Which box is kept fourth from the top?
- Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F?
