Rigorous way to solve the river crossing problem
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I encountered this classic brain teaser:
Four people, A, B, C and D need to get across a river. The only way to
cross the river is by an old bridge, which holds at most 2 people at a
time. Being dark, they can't cross the bridge without a torch, of
which they only have one. So each pair can only walk at the speed of
the slower person. They need to get all of them across to the other
side as quickly as possible. A is the slowest and takes 10 minutes to
cross; B takes 5 minutes; C takes 2 minutes; and D takes 1 minute.
After trying different combinations of paths, the paths that seems to give the smallest time seem to be: CD -> C -> AB -> D -> CD or CD -> D -> AB -> C -> CD
which both give 17 minutes. All other combinations give times that are higher than 17 minutes.
However, is there a systematic way (more rigorous) way to tackle this problem?
river-crossing
asked 6 mins ago
VictorVictor
1
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add a comment |
$begingroup$
I encountered this classic brain teaser:
Four people, A, B, C and D need to get across a river. The only way to
cross the river is by an old bridge, which holds at most 2 people at a
time. Being dark, they can't cross the bridge without a torch, of
which they only have one. So each pair can only walk at the speed of
the slower person. They need to get all of them across to the other
side as quickly as possible. A is the slowest and takes 10 minutes to
cross; B takes 5 minutes; C takes 2 minutes; and D takes 1 minute.
After trying different combinations of paths, the paths that seems to give the smallest time seem to be: CD -> C -> AB -> D -> CD or CD -> D -> AB -> C -> CD
which both give 17 minutes. All other combinations give times that are higher than 17 minutes.
However, is there a systematic way (more rigorous) way to tackle this problem?
river-crossing
asked 6 mins ago
VictorVictor
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I encountered this classic brain teaser:
Four people, A, B, C and D need to get across a river. The only way to
cross the river is by an old bridge, which holds at most 2 people at a
time. Being dark, they can't cross the bridge without a torch, of
which they only have one. So each pair can only walk at the speed of
the slower person. They need to get all of them across to the other
side as quickly as possible. A is the slowest and takes 10 minutes to
cross; B takes 5 minutes; C takes 2 minutes; and D takes 1 minute.
After trying different combinations of paths, the paths that seems to give the smallest time seem to be: CD -> C -> AB -> D -> CD or CD -> D -> AB -> C -> CD
which both give 17 minutes. All other combinations give times that are higher than 17 minutes.
However, is there a systematic way (more rigorous) way to tackle this problem?
river-crossing
asked 6 mins ago
VictorVictor
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I encountered this classic brain teaser:
Four people, A, B, C and D need to get across a river. The only way to
cross the river is by an old bridge, which holds at most 2 people at a
time. Being dark, they can't cross the bridge without a torch, of
which they only have one. So each pair can only walk at the speed of
the slower person. They need to get all of them across to the other
side as quickly as possible. A is the slowest and takes 10 minutes to
cross; B takes 5 minutes; C takes 2 minutes; and D takes 1 minute.
After trying different combinations of paths, the paths that seems to give the smallest time seem to be: CD -> C -> AB -> D -> CD or CD -> D -> AB -> C -> CD
which both give 17 minutes. All other combinations give times that are higher than 17 minutes.
However, is there a systematic way (more rigorous) way to tackle this problem?
river-crossing
river-crossing
asked 6 mins ago
VictorVictor
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
VictorVictor
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
VictorVictor
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
VictorVictor
1
asked 6 mins ago
VictorVictor
1
1
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Victor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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