The Wires Underground [duplicate]Labeling wires in a bundleThe grades of the students in a classA puzzle of...
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The Wires Underground [duplicate]
Labeling wires in a bundleThe grades of the students in a classA puzzle of trust and lies, allies and spiesSink the SubmarineThe Magic Money MachineLabeling wires in a bundleMr. Hilbert and the Problem of the Rogue ResistorThe game of Shafiqa and HabibiA way to beat the system?A Strategy Game Involving Conquering of RegionsThe Alchemist's brewSolution or Origin of logic puzzle
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This question already has an answer here:
Labeling wires in a bundle
5 answers
There are ten wires that run underground across a river. Thus on each of the banks, there are ten ends of the wires. Unfortunately, given an end of a wire on this bank, one doesn't know which end on the other bank it corresponds to. Suppose that you an ohmmeter and a bunch of wires. (You can then, for example, connect two ends on side A of the river, and go to the side B and measure the resistance between every pair of ends to figure out which pair on side B corresponds to the pair that is connected on side A). What is the minimum number of crossings you need to make in order to figure out the matching ends of all the ten wires?
strategy
edited 15 hours ago
athin
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asked 15 hours ago
dvcdvc
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marked as duplicate by boboquack, Rubio♦ 1 hour ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Labeling wires in a bundle
5 answers
There are ten wires that run underground across a river. Thus on each of the banks, there are ten ends of the wires. Unfortunately, given an end of a wire on this bank, one doesn't know which end on the other bank it corresponds to. Suppose that you an ohmmeter and a bunch of wires. (You can then, for example, connect two ends on side A of the river, and go to the side B and measure the resistance between every pair of ends to figure out which pair on side B corresponds to the pair that is connected on side A). What is the minimum number of crossings you need to make in order to figure out the matching ends of all the ten wires?
strategy
edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
asked 15 hours ago
dvcdvc
311 bronze badge
New contributor
dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
marked as duplicate by boboquack, Rubio♦ 1 hour ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
This must be a duplicate
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– Dr Xorile
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago
add a comment |
$begingroup$
This question already has an answer here:
Labeling wires in a bundle
5 answers
There are ten wires that run underground across a river. Thus on each of the banks, there are ten ends of the wires. Unfortunately, given an end of a wire on this bank, one doesn't know which end on the other bank it corresponds to. Suppose that you an ohmmeter and a bunch of wires. (You can then, for example, connect two ends on side A of the river, and go to the side B and measure the resistance between every pair of ends to figure out which pair on side B corresponds to the pair that is connected on side A). What is the minimum number of crossings you need to make in order to figure out the matching ends of all the ten wires?
strategy
edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
asked 15 hours ago
dvcdvc
311 bronze badge
New contributor
dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
This question already has an answer here:
Labeling wires in a bundle
5 answers
There are ten wires that run underground across a river. Thus on each of the banks, there are ten ends of the wires. Unfortunately, given an end of a wire on this bank, one doesn't know which end on the other bank it corresponds to. Suppose that you an ohmmeter and a bunch of wires. (You can then, for example, connect two ends on side A of the river, and go to the side B and measure the resistance between every pair of ends to figure out which pair on side B corresponds to the pair that is connected on side A). What is the minimum number of crossings you need to make in order to figure out the matching ends of all the ten wires?
This question already has an answer here:
Labeling wires in a bundle
5 answers
strategy
strategy
edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
asked 15 hours ago
dvcdvc
311 bronze badge
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dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
asked 15 hours ago
dvcdvc
311 bronze badge
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dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
edited 15 hours ago
athin
13.3k3 gold badges41 silver badges108 bronze badges
13.3k3 gold badges41 silver badges108 bronze badges
asked 15 hours ago
dvcdvc
311 bronze badge
New contributor
dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 15 hours ago
dvcdvc
311 bronze badge
asked 15 hours ago
dvcdvc
311 bronze badge
311 bronze badge
New contributor
dvc is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
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Check out our Code of Conduct.
marked as duplicate by boboquack, Rubio♦ 1 hour ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by boboquack, Rubio♦ 1 hour ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by boboquack, Rubio♦ 1 hour ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
This must be a duplicate
$endgroup$
– Dr Xorile
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago
add a comment |
$begingroup$
This must be a duplicate
$endgroup$
– Dr Xorile
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago
$begingroup$
This must be a duplicate
$endgroup$
– Dr Xorile
14 hours ago
$begingroup$
This must be a duplicate
$endgroup$
– Dr Xorile
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
To solve the problem, at least I can cross
$7$ times.
And the strategy is:
- Connect two wires, says wire $1$ and $2$, then cross.
- Find the corresponding connected wires of $1$ and $2$. Connect another two wires $3$ and $4$, then cross.
- Find the corresponding connected wires of $3$ and $4$. Connect another two wires $5$ and $6$, then cross.
- Find the corresponding connected wires of $5$ and $6$. Connect another two wires $7$ and $8$, then cross.
- Find the corresponding connected wires of $7$ and $8$. You also know which two lefts are $9$ and $10$. Now, connect wires corresponding to $1$ and $3$, then cross.
- Find the corresponding connected wires of $1$ and $3$. You also know for sure about $1$, $2$, $3$, and $4$. Now, connect wires corresponding to $5$ and $7$, then cross.
- Find the corresponding connected wires of $5$ and $7$. You also know for sure about $5$, $6$, $7$, and $8$. Now, connect wires corresponding to $2$ and $9$, then cross.
- Find the corresponding connected wires of $2$ and $9$. You also know for sure about $9$ and $10$.
For improvement, if
I can pair more than once, after the fourth crossing, I can just pair $1$ and $3$, $5$ and $7$, also $2$ and $9$ simultaneously. So I can cross only $5$ times.
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
$endgroup$
add a comment |
$begingroup$
The absolute minimum is
2 crossings
First some observations:
Notice that when you connect ends of wires together, you are forming a partition. Notice that 10 is a triangular number, that is 10 = 1 + 2 + 3 + 4
The actual strategy:
So, first group wires into groups of one, two, three and four. Cross the river. You will be able to identify each group by continuity.
Next
Take one from each group, and form a group of four that way. Then take one from the remaining 3 groups, and so on. Once again, you have formed four differently sized groups, which will be identifiable once you cross the river. Additionally, since each group is formed by members of different groups, you will be able to tell which one is which.
Proof:
It obviously can't be solved with one crossing, as that would mean that you can connect the wires somehow on one end, and read something different on each wire.
answered 11 hours ago
dratini0dratini0
411 bronze badge
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add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
To solve the problem, at least I can cross
$7$ times.
And the strategy is:
- Connect two wires, says wire $1$ and $2$, then cross.
- Find the corresponding connected wires of $1$ and $2$. Connect another two wires $3$ and $4$, then cross.
- Find the corresponding connected wires of $3$ and $4$. Connect another two wires $5$ and $6$, then cross.
- Find the corresponding connected wires of $5$ and $6$. Connect another two wires $7$ and $8$, then cross.
- Find the corresponding connected wires of $7$ and $8$. You also know which two lefts are $9$ and $10$. Now, connect wires corresponding to $1$ and $3$, then cross.
- Find the corresponding connected wires of $1$ and $3$. You also know for sure about $1$, $2$, $3$, and $4$. Now, connect wires corresponding to $5$ and $7$, then cross.
- Find the corresponding connected wires of $5$ and $7$. You also know for sure about $5$, $6$, $7$, and $8$. Now, connect wires corresponding to $2$ and $9$, then cross.
- Find the corresponding connected wires of $2$ and $9$. You also know for sure about $9$ and $10$.
For improvement, if
I can pair more than once, after the fourth crossing, I can just pair $1$ and $3$, $5$ and $7$, also $2$ and $9$ simultaneously. So I can cross only $5$ times.
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
$endgroup$
add a comment |
$begingroup$
To solve the problem, at least I can cross
$7$ times.
And the strategy is:
- Connect two wires, says wire $1$ and $2$, then cross.
- Find the corresponding connected wires of $1$ and $2$. Connect another two wires $3$ and $4$, then cross.
- Find the corresponding connected wires of $3$ and $4$. Connect another two wires $5$ and $6$, then cross.
- Find the corresponding connected wires of $5$ and $6$. Connect another two wires $7$ and $8$, then cross.
- Find the corresponding connected wires of $7$ and $8$. You also know which two lefts are $9$ and $10$. Now, connect wires corresponding to $1$ and $3$, then cross.
- Find the corresponding connected wires of $1$ and $3$. You also know for sure about $1$, $2$, $3$, and $4$. Now, connect wires corresponding to $5$ and $7$, then cross.
- Find the corresponding connected wires of $5$ and $7$. You also know for sure about $5$, $6$, $7$, and $8$. Now, connect wires corresponding to $2$ and $9$, then cross.
- Find the corresponding connected wires of $2$ and $9$. You also know for sure about $9$ and $10$.
For improvement, if
I can pair more than once, after the fourth crossing, I can just pair $1$ and $3$, $5$ and $7$, also $2$ and $9$ simultaneously. So I can cross only $5$ times.
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
$endgroup$
add a comment |
$begingroup$
To solve the problem, at least I can cross
$7$ times.
And the strategy is:
- Connect two wires, says wire $1$ and $2$, then cross.
- Find the corresponding connected wires of $1$ and $2$. Connect another two wires $3$ and $4$, then cross.
- Find the corresponding connected wires of $3$ and $4$. Connect another two wires $5$ and $6$, then cross.
- Find the corresponding connected wires of $5$ and $6$. Connect another two wires $7$ and $8$, then cross.
- Find the corresponding connected wires of $7$ and $8$. You also know which two lefts are $9$ and $10$. Now, connect wires corresponding to $1$ and $3$, then cross.
- Find the corresponding connected wires of $1$ and $3$. You also know for sure about $1$, $2$, $3$, and $4$. Now, connect wires corresponding to $5$ and $7$, then cross.
- Find the corresponding connected wires of $5$ and $7$. You also know for sure about $5$, $6$, $7$, and $8$. Now, connect wires corresponding to $2$ and $9$, then cross.
- Find the corresponding connected wires of $2$ and $9$. You also know for sure about $9$ and $10$.
For improvement, if
I can pair more than once, after the fourth crossing, I can just pair $1$ and $3$, $5$ and $7$, also $2$ and $9$ simultaneously. So I can cross only $5$ times.
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
$endgroup$
To solve the problem, at least I can cross
$7$ times.
And the strategy is:
- Connect two wires, says wire $1$ and $2$, then cross.
- Find the corresponding connected wires of $1$ and $2$. Connect another two wires $3$ and $4$, then cross.
- Find the corresponding connected wires of $3$ and $4$. Connect another two wires $5$ and $6$, then cross.
- Find the corresponding connected wires of $5$ and $6$. Connect another two wires $7$ and $8$, then cross.
- Find the corresponding connected wires of $7$ and $8$. You also know which two lefts are $9$ and $10$. Now, connect wires corresponding to $1$ and $3$, then cross.
- Find the corresponding connected wires of $1$ and $3$. You also know for sure about $1$, $2$, $3$, and $4$. Now, connect wires corresponding to $5$ and $7$, then cross.
- Find the corresponding connected wires of $5$ and $7$. You also know for sure about $5$, $6$, $7$, and $8$. Now, connect wires corresponding to $2$ and $9$, then cross.
- Find the corresponding connected wires of $2$ and $9$. You also know for sure about $9$ and $10$.
For improvement, if
I can pair more than once, after the fourth crossing, I can just pair $1$ and $3$, $5$ and $7$, also $2$ and $9$ simultaneously. So I can cross only $5$ times.
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
answered 14 hours ago
athinathin
13.3k3 gold badges41 silver badges108 bronze badges
13.3k3 gold badges41 silver badges108 bronze badges
add a comment |
add a comment |
$begingroup$
The absolute minimum is
2 crossings
First some observations:
Notice that when you connect ends of wires together, you are forming a partition. Notice that 10 is a triangular number, that is 10 = 1 + 2 + 3 + 4
The actual strategy:
So, first group wires into groups of one, two, three and four. Cross the river. You will be able to identify each group by continuity.
Next
Take one from each group, and form a group of four that way. Then take one from the remaining 3 groups, and so on. Once again, you have formed four differently sized groups, which will be identifiable once you cross the river. Additionally, since each group is formed by members of different groups, you will be able to tell which one is which.
Proof:
It obviously can't be solved with one crossing, as that would mean that you can connect the wires somehow on one end, and read something different on each wire.
answered 11 hours ago
dratini0dratini0
411 bronze badge
New contributor
dratini0 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 |
$begingroup$
The absolute minimum is
2 crossings
First some observations:
Notice that when you connect ends of wires together, you are forming a partition. Notice that 10 is a triangular number, that is 10 = 1 + 2 + 3 + 4
The actual strategy:
So, first group wires into groups of one, two, three and four. Cross the river. You will be able to identify each group by continuity.
Next
Take one from each group, and form a group of four that way. Then take one from the remaining 3 groups, and so on. Once again, you have formed four differently sized groups, which will be identifiable once you cross the river. Additionally, since each group is formed by members of different groups, you will be able to tell which one is which.
Proof:
It obviously can't be solved with one crossing, as that would mean that you can connect the wires somehow on one end, and read something different on each wire.
answered 11 hours ago
dratini0dratini0
411 bronze badge
New contributor
dratini0 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 |
$begingroup$
The absolute minimum is
2 crossings
First some observations:
Notice that when you connect ends of wires together, you are forming a partition. Notice that 10 is a triangular number, that is 10 = 1 + 2 + 3 + 4
The actual strategy:
So, first group wires into groups of one, two, three and four. Cross the river. You will be able to identify each group by continuity.
Next
Take one from each group, and form a group of four that way. Then take one from the remaining 3 groups, and so on. Once again, you have formed four differently sized groups, which will be identifiable once you cross the river. Additionally, since each group is formed by members of different groups, you will be able to tell which one is which.
Proof:
It obviously can't be solved with one crossing, as that would mean that you can connect the wires somehow on one end, and read something different on each wire.
answered 11 hours ago
dratini0dratini0
411 bronze badge
New contributor
dratini0 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
The absolute minimum is
2 crossings
First some observations:
Notice that when you connect ends of wires together, you are forming a partition. Notice that 10 is a triangular number, that is 10 = 1 + 2 + 3 + 4
The actual strategy:
So, first group wires into groups of one, two, three and four. Cross the river. You will be able to identify each group by continuity.
Next
Take one from each group, and form a group of four that way. Then take one from the remaining 3 groups, and so on. Once again, you have formed four differently sized groups, which will be identifiable once you cross the river. Additionally, since each group is formed by members of different groups, you will be able to tell which one is which.
Proof:
It obviously can't be solved with one crossing, as that would mean that you can connect the wires somehow on one end, and read something different on each wire.
answered 11 hours ago
dratini0dratini0
411 bronze badge
New contributor
dratini0 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 11 hours ago
dratini0dratini0
411 bronze badge
New contributor
dratini0 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 11 hours ago
dratini0dratini0
411 bronze badge
answered 11 hours ago
dratini0dratini0
411 bronze badge
411 bronze badge
New contributor
dratini0 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
dratini0 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 |
$begingroup$
This must be a duplicate
$endgroup$
– Dr Xorile
14 hours ago
$begingroup$
What counts as one wiring? If I connect end A1 to A2 and B1 to B2 is that two and then measure the resistance between A1 and B1, is that one wiring or two?
$endgroup$
– Helena
14 hours ago
$begingroup$
Possible duplicate of Labeling wires in a bundle (@DrXorile)
$endgroup$
– boboquack
1 hour ago