Wolves and sheep The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fastest way to collect an arbitrary armyMiddle weight puzzleA puzzle of trust and lies, allies and spiesCooperative guessing against an evil godLabeling wires in a *damaged* bundleMonopoly Game Show: Is there a winning strategy?Picking A Number GamePrisoners and minority votingMove 10 sheep on another shoreBlindfold Bingo
How do I add random spotting to the same face in cycles?
Can a 1st-level character have an ability score above 18?
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
Change bounding box of math glyphs in LuaTeX
Is there a writing software that you can sort scenes like slides in PowerPoint?
What are these Gizmos at Izaña Atmospheric Research Center in Spain?
Working through the single responsibility principle (SRP) in Python when calls are expensive
Is above average number of years spent on PhD considered a red flag in future academia or industry positions?
Am I ethically obligated to go into work on an off day if the reason is sudden?
When did F become S in typeography, and why?
I could not break this equation. Please help me
How did passengers keep warm on sail ships?
Keeping a retro style to sci-fi spaceships?
How to split my screen on my Macbook Air?
What was the last x86 CPU that did not have the x87 floating-point unit built in?
How do you keep chess fun when your opponent constantly beats you?
Segmentation fault output is suppressed when piping stdin into a function. Why?
Why did all the guest students take carriages to the Yule Ball?
Arduino Pro Micro - switch off LEDs
Typeface like Times New Roman but with "tied" percent sign
How to pronounce 1ターン?
Is every episode of "Where are my Pants?" identical?
Is this wall load bearing? Blueprints and photos attached
How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time
Wolves and sheep
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fastest way to collect an arbitrary armyMiddle weight puzzleA puzzle of trust and lies, allies and spiesCooperative guessing against an evil godLabeling wires in a *damaged* bundleMonopoly Game Show: Is there a winning strategy?Picking A Number GamePrisoners and minority votingMove 10 sheep on another shoreBlindfold Bingo
$begingroup$
All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.
To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:
From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.
Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.
I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.
One caveat is that the test results are available to you after all the tests are done!
Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.
Can you help the king by devising a strategy?
strategy combinatorics algorithm
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
$endgroup$
add a comment |
$begingroup$
All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.
To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:
From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.
Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.
I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.
One caveat is that the test results are available to you after all the tests are done!
Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.
Can you help the king by devising a strategy?
strategy combinatorics algorithm
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
$endgroup$
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago
add a comment |
$begingroup$
All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.
To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:
From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.
Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.
I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.
One caveat is that the test results are available to you after all the tests are done!
Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.
Can you help the king by devising a strategy?
strategy combinatorics algorithm
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
$endgroup$
All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.
To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:
From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.
Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.
I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.
One caveat is that the test results are available to you after all the tests are done!
Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.
Can you help the king by devising a strategy?
strategy combinatorics algorithm
strategy combinatorics algorithm
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
asked 3 hours ago
Jyotish RobinJyotish Robin
515112
515112
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago
add a comment |
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Here's my shot at it:
Pool 50 of the sheep. Of those 50, if the result comes back positive (wolf detected), split in half again, testing 25 pooled together. If this comes back positive, either 12 or 13 ofthe positive group. You see where this is going. Any negative results rule out all sheep in that group. Worst case scenario, it takes 54 tests (see image for explanation). Best case scenario, you get 14 tests. Price range: 14,000 - 54,000 dollars.
Not sure yet of the expected average, but I know this is better than 99 tests on average.
Diagram:
If this isn't the optimal solution, then my best bet on how to improve it would be to:
split into 1/5 the size of each group.
answered 46 mins ago
user45266user45266
32514
$endgroup$
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
add a comment |
$begingroup$
There must be better algorithms, but just to put an upper bound on a solution, the worst case scenario can be reduced to
35 tests. Do binary searches for one wolf. Each search is done on all the sheep minus wolfs found in the previous searches. So the first binary search is done on a set of all 100 'sheep'. You will find a wolf in no more than 7 tests. The next binary search is done on remaining 99 sheep. And so on. You will need 5 binary searches. Each search will take at most 7 tests. So the worst case scenario is 35 tests.
answered 9 mins ago
ppgdevppgdev
41516
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "559"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f81737%2fwolves-and-sheep%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Here's my shot at it:
Pool 50 of the sheep. Of those 50, if the result comes back positive (wolf detected), split in half again, testing 25 pooled together. If this comes back positive, either 12 or 13 ofthe positive group. You see where this is going. Any negative results rule out all sheep in that group. Worst case scenario, it takes 54 tests (see image for explanation). Best case scenario, you get 14 tests. Price range: 14,000 - 54,000 dollars.
Not sure yet of the expected average, but I know this is better than 99 tests on average.
Diagram:
If this isn't the optimal solution, then my best bet on how to improve it would be to:
split into 1/5 the size of each group.
answered 46 mins ago
user45266user45266
32514
$endgroup$
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
add a comment |
$begingroup$
Here's my shot at it:
Pool 50 of the sheep. Of those 50, if the result comes back positive (wolf detected), split in half again, testing 25 pooled together. If this comes back positive, either 12 or 13 ofthe positive group. You see where this is going. Any negative results rule out all sheep in that group. Worst case scenario, it takes 54 tests (see image for explanation). Best case scenario, you get 14 tests. Price range: 14,000 - 54,000 dollars.
Not sure yet of the expected average, but I know this is better than 99 tests on average.
Diagram:
If this isn't the optimal solution, then my best bet on how to improve it would be to:
split into 1/5 the size of each group.
answered 46 mins ago
user45266user45266
32514
$endgroup$
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
add a comment |
$begingroup$
Here's my shot at it:
Pool 50 of the sheep. Of those 50, if the result comes back positive (wolf detected), split in half again, testing 25 pooled together. If this comes back positive, either 12 or 13 ofthe positive group. You see where this is going. Any negative results rule out all sheep in that group. Worst case scenario, it takes 54 tests (see image for explanation). Best case scenario, you get 14 tests. Price range: 14,000 - 54,000 dollars.
Not sure yet of the expected average, but I know this is better than 99 tests on average.
Diagram:
If this isn't the optimal solution, then my best bet on how to improve it would be to:
split into 1/5 the size of each group.
answered 46 mins ago
user45266user45266
32514
$endgroup$
Here's my shot at it:
Pool 50 of the sheep. Of those 50, if the result comes back positive (wolf detected), split in half again, testing 25 pooled together. If this comes back positive, either 12 or 13 ofthe positive group. You see where this is going. Any negative results rule out all sheep in that group. Worst case scenario, it takes 54 tests (see image for explanation). Best case scenario, you get 14 tests. Price range: 14,000 - 54,000 dollars.
Not sure yet of the expected average, but I know this is better than 99 tests on average.
Diagram:
If this isn't the optimal solution, then my best bet on how to improve it would be to:
split into 1/5 the size of each group.
answered 46 mins ago
user45266user45266
32514
answered 46 mins ago
user45266user45266
32514
answered 46 mins ago
user45266user45266
32514
answered 46 mins ago
user45266user45266
32514
32514
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
add a comment |
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
I do not consider it much of a spoiler (there must be better algorithms) but the worst case scenario can be easily reduced to 35 tests. rot13(Qb ovanel frnepurf sbe bar jbys. Rnpu frnepu vf qbar ba nyy gur furrc zvahf jbysf sbhaq va gur cerivbhf frnepurf. Lbh jvyy arrq 5 frnepurf. Rnpu frnepu jvyy gnxr ng zbfg 7 grfgf. Fb gur jbefg pnfr fpranevb vf 35 grfgf).
$endgroup$
– ppgdev
28 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
Wait a minute, how would that work? Could you be a little more specific?
$endgroup$
– user45266
26 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
@ppgdev Like starting with 100, you split the group into 5 groups? What do you mean?
$endgroup$
– user45266
24 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
$begingroup$
I moved my comment into an upper bound answer, with a more detailed explanation.
$endgroup$
– ppgdev
8 mins ago
add a comment |
$begingroup$
There must be better algorithms, but just to put an upper bound on a solution, the worst case scenario can be reduced to
35 tests. Do binary searches for one wolf. Each search is done on all the sheep minus wolfs found in the previous searches. So the first binary search is done on a set of all 100 'sheep'. You will find a wolf in no more than 7 tests. The next binary search is done on remaining 99 sheep. And so on. You will need 5 binary searches. Each search will take at most 7 tests. So the worst case scenario is 35 tests.
answered 9 mins ago
ppgdevppgdev
41516
$endgroup$
add a comment |
$begingroup$
There must be better algorithms, but just to put an upper bound on a solution, the worst case scenario can be reduced to
35 tests. Do binary searches for one wolf. Each search is done on all the sheep minus wolfs found in the previous searches. So the first binary search is done on a set of all 100 'sheep'. You will find a wolf in no more than 7 tests. The next binary search is done on remaining 99 sheep. And so on. You will need 5 binary searches. Each search will take at most 7 tests. So the worst case scenario is 35 tests.
answered 9 mins ago
ppgdevppgdev
41516
$endgroup$
add a comment |
$begingroup$
There must be better algorithms, but just to put an upper bound on a solution, the worst case scenario can be reduced to
35 tests. Do binary searches for one wolf. Each search is done on all the sheep minus wolfs found in the previous searches. So the first binary search is done on a set of all 100 'sheep'. You will find a wolf in no more than 7 tests. The next binary search is done on remaining 99 sheep. And so on. You will need 5 binary searches. Each search will take at most 7 tests. So the worst case scenario is 35 tests.
answered 9 mins ago
ppgdevppgdev
41516
$endgroup$
There must be better algorithms, but just to put an upper bound on a solution, the worst case scenario can be reduced to
35 tests. Do binary searches for one wolf. Each search is done on all the sheep minus wolfs found in the previous searches. So the first binary search is done on a set of all 100 'sheep'. You will find a wolf in no more than 7 tests. The next binary search is done on remaining 99 sheep. And so on. You will need 5 binary searches. Each search will take at most 7 tests. So the worst case scenario is 35 tests.
answered 9 mins ago
ppgdevppgdev
41516
answered 9 mins ago
ppgdevppgdev
41516
answered 9 mins ago
ppgdevppgdev
41516
answered 9 mins ago
ppgdevppgdev
41516
41516
add a comment |
add a comment |
Thanks for contributing an answer to Puzzling Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f81737%2fwolves-and-sheep%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
This is close to a covering design (Lotto wheel) problem.
$endgroup$
– Arnaud Mortier
3 hours ago
$begingroup$
First of all, does the government have enough funds to test 99 of the sheep? Because that would work, at a cost of $99,000. Congrats, you just saved 1,000 bucks.
$endgroup$
– user45266
55 mins ago
$begingroup$
Alternatively, you know the location of all 5 wolves. Take initiative and slaughter all 100. Now you have no more wolves, and food for a good while to come.
$endgroup$
– user45266
43 mins ago