Island of LiarsKill the jokers! - Part 1Kill the jokers! - Part 2Another village of liars and truth-tellersLiar and the Truth teller with 6 inhabitantsThree truth teller boys on an islandWho led the mutiny?What did he say he said? Liars with a twist!How many liars are in the room?Liar liar pants on fireRound tabel conference with liars?
Why is Collection not simply treated as Collection<?>
How much of data wrangling is a data scientist's job?
What's the point of deactivating Num Lock on login screens?
I Accidentally Deleted a Stock Terminal Theme
Is it legal for company to use my work email to pretend I still work there?
Why are electrically insulating heatsinks so rare? Is it just cost?
Blender 2.8 I can't see vertices, edges or faces in edit mode
Has there ever been an airliner design involving reducing generator load by installing solar panels?
Why doesn't H₄O²⁺ exist?
Can one be a co-translator of a book, if he does not know the language that the book is translated into?
Is it possible to create light that imparts a greater proportion of its energy as momentum rather than heat?
Where does SFDX store details about scratch orgs?
Western buddy movie with a supernatural twist where a woman turns into an eagle at the end
Why does ы have a soft sign in it?
Were any external disk drives stacked vertically?
How do I find out when a node was added to an availability group?
How can I tell someone that I want to be his or her friend?
Why do I get two different answers for this counting problem?
Why can't we play rap on piano?
Infinite Abelian subgroup of infinite non Abelian group example
Issue with type force PATH search
Emailing HOD to enhance faculty application
Brothers & sisters
Why does Optional.map make this assignment work?
Island of Liars
Kill the jokers! - Part 1Kill the jokers! - Part 2Another village of liars and truth-tellersLiar and the Truth teller with 6 inhabitantsThree truth teller boys on an islandWho led the mutiny?What did he say he said? Liars with a twist!How many liars are in the room?Liar liar pants on fireRound tabel conference with liars?
$begingroup$
A king goes to an island, where there are 5823 people who always tell the truth and 8723 who always lie.
The king is special guest for the party celebrating 2053 year.
On the party, liars and truth tellers dance in couples (everyone can dance with everyone), some people leave the dance, others join and some don't even participate in the dances as they are not dance lovers.
After the party, the king asked everyone who had danced on the party, how many truth tellers did he dance with and put the numbers into his diary.
Surprisingly, when he checked his diary later on, he found out he had all the numbers from 0 to 956 typed in uniquely.
How many truth tellers danced on the party, assuming everyone knows who is truth teller and who is liar?
mathematics liars
edited Mar 27 at 9:54
jafe
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
$endgroup$
add a comment |
$begingroup$
A king goes to an island, where there are 5823 people who always tell the truth and 8723 who always lie.
The king is special guest for the party celebrating 2053 year.
On the party, liars and truth tellers dance in couples (everyone can dance with everyone), some people leave the dance, others join and some don't even participate in the dances as they are not dance lovers.
After the party, the king asked everyone who had danced on the party, how many truth tellers did he dance with and put the numbers into his diary.
Surprisingly, when he checked his diary later on, he found out he had all the numbers from 0 to 956 typed in uniquely.
How many truth tellers danced on the party, assuming everyone knows who is truth teller and who is liar?
mathematics liars
edited Mar 27 at 9:54
jafe
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
$endgroup$
3
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
1
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
add a comment |
$begingroup$
A king goes to an island, where there are 5823 people who always tell the truth and 8723 who always lie.
The king is special guest for the party celebrating 2053 year.
On the party, liars and truth tellers dance in couples (everyone can dance with everyone), some people leave the dance, others join and some don't even participate in the dances as they are not dance lovers.
After the party, the king asked everyone who had danced on the party, how many truth tellers did he dance with and put the numbers into his diary.
Surprisingly, when he checked his diary later on, he found out he had all the numbers from 0 to 956 typed in uniquely.
How many truth tellers danced on the party, assuming everyone knows who is truth teller and who is liar?
mathematics liars
edited Mar 27 at 9:54
jafe
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
$endgroup$
A king goes to an island, where there are 5823 people who always tell the truth and 8723 who always lie.
The king is special guest for the party celebrating 2053 year.
On the party, liars and truth tellers dance in couples (everyone can dance with everyone), some people leave the dance, others join and some don't even participate in the dances as they are not dance lovers.
After the party, the king asked everyone who had danced on the party, how many truth tellers did he dance with and put the numbers into his diary.
Surprisingly, when he checked his diary later on, he found out he had all the numbers from 0 to 956 typed in uniquely.
How many truth tellers danced on the party, assuming everyone knows who is truth teller and who is liar?
mathematics liars
mathematics liars
edited Mar 27 at 9:54
jafe
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
edited Mar 27 at 9:54
jafe
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
edited Mar 27 at 9:54
jafe
25.1k472249
edited Mar 27 at 9:54
jafe
25.1k472249
edited Mar 27 at 9:54
jafe
25.1k472249
25.1k472249
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
asked Mar 27 at 9:25
Kradec na kysmetKradec na kysmet
817
817
3
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
1
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
add a comment |
3
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
1
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
3
3
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
1
1
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I think that the answer is
Just $1$ truthteller danced.
Reasoning
Suppose more than one truthteller dances, say $N$. Now consider the graph of dancers just involving truthtellers, where an edge represents "danced with". Within this graph, either the lowest degree of a node is $0$, where then the highest possible is $N-2$, or the lowest degree is $1$, where the highest possible is $N-1$. In either case, by the Pigeonhole Principle, there will be at least two truthtellers who report the same number to the king. Of course, if there are zero truthtellers who danced then one of the liars would have to have told the truth - saying $0$.
Proof that this works
Suppose there is $1$ truthteller, he will report $0$. There just needs to be one liar who doesn't dance with the truthteller who reports $1$. Then everyone else is verifiably lying.
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
$endgroup$
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
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');
);
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%2f81070%2fisland-of-liars%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I think that the answer is
Just $1$ truthteller danced.
Reasoning
Suppose more than one truthteller dances, say $N$. Now consider the graph of dancers just involving truthtellers, where an edge represents "danced with". Within this graph, either the lowest degree of a node is $0$, where then the highest possible is $N-2$, or the lowest degree is $1$, where the highest possible is $N-1$. In either case, by the Pigeonhole Principle, there will be at least two truthtellers who report the same number to the king. Of course, if there are zero truthtellers who danced then one of the liars would have to have told the truth - saying $0$.
Proof that this works
Suppose there is $1$ truthteller, he will report $0$. There just needs to be one liar who doesn't dance with the truthteller who reports $1$. Then everyone else is verifiably lying.
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
$endgroup$
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
add a comment |
$begingroup$
I think that the answer is
Just $1$ truthteller danced.
Reasoning
Suppose more than one truthteller dances, say $N$. Now consider the graph of dancers just involving truthtellers, where an edge represents "danced with". Within this graph, either the lowest degree of a node is $0$, where then the highest possible is $N-2$, or the lowest degree is $1$, where the highest possible is $N-1$. In either case, by the Pigeonhole Principle, there will be at least two truthtellers who report the same number to the king. Of course, if there are zero truthtellers who danced then one of the liars would have to have told the truth - saying $0$.
Proof that this works
Suppose there is $1$ truthteller, he will report $0$. There just needs to be one liar who doesn't dance with the truthteller who reports $1$. Then everyone else is verifiably lying.
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
$endgroup$
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
add a comment |
$begingroup$
I think that the answer is
Just $1$ truthteller danced.
Reasoning
Suppose more than one truthteller dances, say $N$. Now consider the graph of dancers just involving truthtellers, where an edge represents "danced with". Within this graph, either the lowest degree of a node is $0$, where then the highest possible is $N-2$, or the lowest degree is $1$, where the highest possible is $N-1$. In either case, by the Pigeonhole Principle, there will be at least two truthtellers who report the same number to the king. Of course, if there are zero truthtellers who danced then one of the liars would have to have told the truth - saying $0$.
Proof that this works
Suppose there is $1$ truthteller, he will report $0$. There just needs to be one liar who doesn't dance with the truthteller who reports $1$. Then everyone else is verifiably lying.
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
$endgroup$
I think that the answer is
Just $1$ truthteller danced.
Reasoning
Suppose more than one truthteller dances, say $N$. Now consider the graph of dancers just involving truthtellers, where an edge represents "danced with". Within this graph, either the lowest degree of a node is $0$, where then the highest possible is $N-2$, or the lowest degree is $1$, where the highest possible is $N-1$. In either case, by the Pigeonhole Principle, there will be at least two truthtellers who report the same number to the king. Of course, if there are zero truthtellers who danced then one of the liars would have to have told the truth - saying $0$.
Proof that this works
Suppose there is $1$ truthteller, he will report $0$. There just needs to be one liar who doesn't dance with the truthteller who reports $1$. Then everyone else is verifiably lying.
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
answered Mar 27 at 9:54
hexominohexomino
45.6k4140219
45.6k4140219
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
add a comment |
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
That's it, that was fast even with all the baits I put.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
@Kradecnakysmet Thanks, I was thrown for a second by the numbers and thought there might be a large number of solutions.
$endgroup$
– hexomino
Mar 27 at 9:59
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
$begingroup$
I will admit I was laughing while typing all those random numbers :D
$endgroup$
– Kradec na kysmet
Mar 27 at 10:00
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');
);
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%2f81070%2fisland-of-liars%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');
);
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');
);
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');
);
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
-liars, mathematics
3
$begingroup$
Just to clarify a few things: 1. Do the liars have to put down a specific number, or can they just write down any number at all as long as it’s not the number of people they danced with? 2. Does the king participate in the dancing? Thanks!
$endgroup$
– PiIsNot3
Mar 27 at 9:37
1
$begingroup$
1. Everyone can type whatever he/she wants as long as it's truth or lie. 2. Doesn't matter if king danced at all.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:47
$begingroup$
Is the King lying? What does a truth-teller say about dancing with the King?
$endgroup$
– Weather Vane
Mar 27 at 9:52
$begingroup$
Got the right answer, but even if the king was liar/truth teller it would still fit in, but no he didn't dance at all, he dislikes dancing.
$endgroup$
– Kradec na kysmet
Mar 27 at 9:57