Treasure Hunt RiddleA Dark But Quite Progressive Puzzle. What's the musical solution to this riddle +...
Why is it that Bernie Sanders is always called a "socialist"?
Does Skippy chunky peanut butter contain trans fat?
Is there a lava-breathing lizard creature (that could be worshipped by a cult) in 5e?
Can polar coordinate cause misalignment in TikZ?
Bash script to truncate subject line of incoming email
How to access internet and run apt-get through a middle server?
What is a good reason for every spaceship to carry a weapon on board?
Could an Apollo mission be possible if Moon would be Earth like?
Why did Luke use his left hand to shoot?
How do you funnel food off a cutting board?
Non-Cancer terminal illness that can affect young (age 10-13) girls?
How do I prevent a homebrew Grappling Hook feature from trivializing Tomb of Annihilation?
Count repetitions of an array
Why zero tolerance on nudity in space?
Why avoid shared user accounts?
Potential client has a problematic employee I can't work with
How to politely refuse in-office gym instructor for steroids and protein
Book where a space ship journeys to the center of the galaxy to find all the stars had gone supernova
Current across a wire with zero potential difference
Does it take energy to move something in a circle?
Is there a verb that means to inject with poison?
What is a DAG (Graph Theory)?
systemd service won't start nodejs
Why is Agricola named as such?
Treasure Hunt Riddle
A Dark But Quite Progressive Puzzle. What's the musical solution to this riddle + cryptogram?A hunt for long forgotten treasure …but beware the pirate's curse!Treasure hunt questionThe Grand Monarch's challengeFind the treasure before Dargloc doesA man walked up on a shoreAnonymous letter from somewhere sometime todayThe Fenn Treasure Hunt (REAL!)Let's have a treasure hunt!The mysterious box: The First Clue
$begingroup$
John and Peter participate in a treasure hunting competition. The organizer places a gold medal in one of the lockers. The locker rack contains 49 lockers, each of which has a name indicating its row and column. The organizer gives both of them a list of 10 possible treasure locker location as shown below. The organizer will tell John the treasure locker row (A to G) and tell Peter the treasure locker column (1 to 7).
John: "I have no idea where the treasure locker is, and I do not think Peter will know.".
Peter: "I have no idea just now, but I know the treasure locker location."
John: "I also know where the treasure locker location is".
So, where is the treasure locker location? Please explain your answer.
riddle
New contributor
$endgroup$
add a comment |
$begingroup$
John and Peter participate in a treasure hunting competition. The organizer places a gold medal in one of the lockers. The locker rack contains 49 lockers, each of which has a name indicating its row and column. The organizer gives both of them a list of 10 possible treasure locker location as shown below. The organizer will tell John the treasure locker row (A to G) and tell Peter the treasure locker column (1 to 7).
John: "I have no idea where the treasure locker is, and I do not think Peter will know.".
Peter: "I have no idea just now, but I know the treasure locker location."
John: "I also know where the treasure locker location is".
So, where is the treasure locker location? Please explain your answer.
riddle
New contributor
$endgroup$
1
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
1
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago
add a comment |
$begingroup$
John and Peter participate in a treasure hunting competition. The organizer places a gold medal in one of the lockers. The locker rack contains 49 lockers, each of which has a name indicating its row and column. The organizer gives both of them a list of 10 possible treasure locker location as shown below. The organizer will tell John the treasure locker row (A to G) and tell Peter the treasure locker column (1 to 7).
John: "I have no idea where the treasure locker is, and I do not think Peter will know.".
Peter: "I have no idea just now, but I know the treasure locker location."
John: "I also know where the treasure locker location is".
So, where is the treasure locker location? Please explain your answer.
riddle
New contributor
$endgroup$
John and Peter participate in a treasure hunting competition. The organizer places a gold medal in one of the lockers. The locker rack contains 49 lockers, each of which has a name indicating its row and column. The organizer gives both of them a list of 10 possible treasure locker location as shown below. The organizer will tell John the treasure locker row (A to G) and tell Peter the treasure locker column (1 to 7).
John: "I have no idea where the treasure locker is, and I do not think Peter will know.".
Peter: "I have no idea just now, but I know the treasure locker location."
John: "I also know where the treasure locker location is".
So, where is the treasure locker location? Please explain your answer.
riddle
riddle
New contributor
New contributor
edited 1 hour ago
Hugh
2,1291925
2,1291925
New contributor
asked 4 hours ago
HugoHugo
262
262
New contributor
New contributor
1
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
1
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago
add a comment |
1
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
1
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago
1
1
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
1
1
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
If John
Doesn’t think Peter will know, he must be sure that the gold medal isn’t in A5 or B3. He therefore mustn’t have been told A or B.
Eliminated lockers:
A2, A5, B3, B6, B7.
The medal is therefore in
rows D or F.
Now, If Peter
was told 1, he still wouldn’t be able to find out the locker after John’s statement, because D1 and F1 are both possible lockers. So the gold medal isn’t there.
More eliminated lockers:
D1, F1
Peter must’ve been told
2, 6, or 7, because he would be able to uniquely determine the locker after John’s statement. There are three possible lockers: F2, D6, and F7.
If John was told
F, then by Peter’s statement, F1 would be eliminated in John’s mind. However, John would not be able to discern between F2 and F7. If John was told D, he would know the locker was D6. This is the only locker where both would know the location given their deductions.
Therefore the gold medal is in
Locker D6.
$endgroup$
add a comment |
$begingroup$
I have a different answer. It might be a little lateral-thinking, but word choice matters! The treasure is in locker:
F2
The first thing to really pay attention to is when John says:
"I do not think Peter will know".
Why didn't he say I know for a fact Peter does not know? Because he does not know for a fact that Peter does not know. It's like when I go with my friend to play roulette and he puts all his money on 32. I try to talk him out of it by saying "take your money back, I do not think 32 will come up". Why did I say that? Do I know for sure 32 will not come up? Of course not, it's just that it's so unlikely that I do not think it will this time. Same with John, he does not know that Peter for sure does not know where the treasure is, it is just that it is unlikely that he does.
Having determined this, the next step is:
So we cannot eliminate row B, because if John was given row B then Peter could have been given columns 3, 6 or 7. Only if he was given column 3 would he know where the treasure is - that's a 33% probability and unlikely to happen in a sense that an even that occurs 66% of the time is more likely to happen than one that occurs only 33% of the time. Right? That is why John says he does not think Peter will know.
The only row we can eliminate is row A. If John was given row A then Peter would have a 50% chance to either know or not know where the treasure is, so John would be unable to say that he doesn't think Peter will know, because with a 50% chance he cannot take a position of what is more likely to happen - Peter knowing or not knowing.
It's a breeze now:
Now Peter says he didn't know where the treasure was, but now he knows. So Peter was not given columns 3 or 5 because then he would know right away. The only way for him to know where the treasure is after only eliminating row A is if the treasure is in F2. Now for John to know where the treasure is after hearing Peter would have to mean that he was given row F and he also deduced that the treasure is in F2.
And that's that.
New contributor
$endgroup$
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
});
}
});
Hugo is a new contributor. Be nice, and check out our Code of Conduct.
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%2f79989%2ftreasure-hunt-riddle%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
$begingroup$
If John
Doesn’t think Peter will know, he must be sure that the gold medal isn’t in A5 or B3. He therefore mustn’t have been told A or B.
Eliminated lockers:
A2, A5, B3, B6, B7.
The medal is therefore in
rows D or F.
Now, If Peter
was told 1, he still wouldn’t be able to find out the locker after John’s statement, because D1 and F1 are both possible lockers. So the gold medal isn’t there.
More eliminated lockers:
D1, F1
Peter must’ve been told
2, 6, or 7, because he would be able to uniquely determine the locker after John’s statement. There are three possible lockers: F2, D6, and F7.
If John was told
F, then by Peter’s statement, F1 would be eliminated in John’s mind. However, John would not be able to discern between F2 and F7. If John was told D, he would know the locker was D6. This is the only locker where both would know the location given their deductions.
Therefore the gold medal is in
Locker D6.
$endgroup$
add a comment |
$begingroup$
If John
Doesn’t think Peter will know, he must be sure that the gold medal isn’t in A5 or B3. He therefore mustn’t have been told A or B.
Eliminated lockers:
A2, A5, B3, B6, B7.
The medal is therefore in
rows D or F.
Now, If Peter
was told 1, he still wouldn’t be able to find out the locker after John’s statement, because D1 and F1 are both possible lockers. So the gold medal isn’t there.
More eliminated lockers:
D1, F1
Peter must’ve been told
2, 6, or 7, because he would be able to uniquely determine the locker after John’s statement. There are three possible lockers: F2, D6, and F7.
If John was told
F, then by Peter’s statement, F1 would be eliminated in John’s mind. However, John would not be able to discern between F2 and F7. If John was told D, he would know the locker was D6. This is the only locker where both would know the location given their deductions.
Therefore the gold medal is in
Locker D6.
$endgroup$
add a comment |
$begingroup$
If John
Doesn’t think Peter will know, he must be sure that the gold medal isn’t in A5 or B3. He therefore mustn’t have been told A or B.
Eliminated lockers:
A2, A5, B3, B6, B7.
The medal is therefore in
rows D or F.
Now, If Peter
was told 1, he still wouldn’t be able to find out the locker after John’s statement, because D1 and F1 are both possible lockers. So the gold medal isn’t there.
More eliminated lockers:
D1, F1
Peter must’ve been told
2, 6, or 7, because he would be able to uniquely determine the locker after John’s statement. There are three possible lockers: F2, D6, and F7.
If John was told
F, then by Peter’s statement, F1 would be eliminated in John’s mind. However, John would not be able to discern between F2 and F7. If John was told D, he would know the locker was D6. This is the only locker where both would know the location given their deductions.
Therefore the gold medal is in
Locker D6.
$endgroup$
If John
Doesn’t think Peter will know, he must be sure that the gold medal isn’t in A5 or B3. He therefore mustn’t have been told A or B.
Eliminated lockers:
A2, A5, B3, B6, B7.
The medal is therefore in
rows D or F.
Now, If Peter
was told 1, he still wouldn’t be able to find out the locker after John’s statement, because D1 and F1 are both possible lockers. So the gold medal isn’t there.
More eliminated lockers:
D1, F1
Peter must’ve been told
2, 6, or 7, because he would be able to uniquely determine the locker after John’s statement. There are three possible lockers: F2, D6, and F7.
If John was told
F, then by Peter’s statement, F1 would be eliminated in John’s mind. However, John would not be able to discern between F2 and F7. If John was told D, he would know the locker was D6. This is the only locker where both would know the location given their deductions.
Therefore the gold medal is in
Locker D6.
answered 4 hours ago
El-GuestEl-Guest
19k24286
19k24286
add a comment |
add a comment |
$begingroup$
I have a different answer. It might be a little lateral-thinking, but word choice matters! The treasure is in locker:
F2
The first thing to really pay attention to is when John says:
"I do not think Peter will know".
Why didn't he say I know for a fact Peter does not know? Because he does not know for a fact that Peter does not know. It's like when I go with my friend to play roulette and he puts all his money on 32. I try to talk him out of it by saying "take your money back, I do not think 32 will come up". Why did I say that? Do I know for sure 32 will not come up? Of course not, it's just that it's so unlikely that I do not think it will this time. Same with John, he does not know that Peter for sure does not know where the treasure is, it is just that it is unlikely that he does.
Having determined this, the next step is:
So we cannot eliminate row B, because if John was given row B then Peter could have been given columns 3, 6 or 7. Only if he was given column 3 would he know where the treasure is - that's a 33% probability and unlikely to happen in a sense that an even that occurs 66% of the time is more likely to happen than one that occurs only 33% of the time. Right? That is why John says he does not think Peter will know.
The only row we can eliminate is row A. If John was given row A then Peter would have a 50% chance to either know or not know where the treasure is, so John would be unable to say that he doesn't think Peter will know, because with a 50% chance he cannot take a position of what is more likely to happen - Peter knowing or not knowing.
It's a breeze now:
Now Peter says he didn't know where the treasure was, but now he knows. So Peter was not given columns 3 or 5 because then he would know right away. The only way for him to know where the treasure is after only eliminating row A is if the treasure is in F2. Now for John to know where the treasure is after hearing Peter would have to mean that he was given row F and he also deduced that the treasure is in F2.
And that's that.
New contributor
$endgroup$
add a comment |
$begingroup$
I have a different answer. It might be a little lateral-thinking, but word choice matters! The treasure is in locker:
F2
The first thing to really pay attention to is when John says:
"I do not think Peter will know".
Why didn't he say I know for a fact Peter does not know? Because he does not know for a fact that Peter does not know. It's like when I go with my friend to play roulette and he puts all his money on 32. I try to talk him out of it by saying "take your money back, I do not think 32 will come up". Why did I say that? Do I know for sure 32 will not come up? Of course not, it's just that it's so unlikely that I do not think it will this time. Same with John, he does not know that Peter for sure does not know where the treasure is, it is just that it is unlikely that he does.
Having determined this, the next step is:
So we cannot eliminate row B, because if John was given row B then Peter could have been given columns 3, 6 or 7. Only if he was given column 3 would he know where the treasure is - that's a 33% probability and unlikely to happen in a sense that an even that occurs 66% of the time is more likely to happen than one that occurs only 33% of the time. Right? That is why John says he does not think Peter will know.
The only row we can eliminate is row A. If John was given row A then Peter would have a 50% chance to either know or not know where the treasure is, so John would be unable to say that he doesn't think Peter will know, because with a 50% chance he cannot take a position of what is more likely to happen - Peter knowing or not knowing.
It's a breeze now:
Now Peter says he didn't know where the treasure was, but now he knows. So Peter was not given columns 3 or 5 because then he would know right away. The only way for him to know where the treasure is after only eliminating row A is if the treasure is in F2. Now for John to know where the treasure is after hearing Peter would have to mean that he was given row F and he also deduced that the treasure is in F2.
And that's that.
New contributor
$endgroup$
add a comment |
$begingroup$
I have a different answer. It might be a little lateral-thinking, but word choice matters! The treasure is in locker:
F2
The first thing to really pay attention to is when John says:
"I do not think Peter will know".
Why didn't he say I know for a fact Peter does not know? Because he does not know for a fact that Peter does not know. It's like when I go with my friend to play roulette and he puts all his money on 32. I try to talk him out of it by saying "take your money back, I do not think 32 will come up". Why did I say that? Do I know for sure 32 will not come up? Of course not, it's just that it's so unlikely that I do not think it will this time. Same with John, he does not know that Peter for sure does not know where the treasure is, it is just that it is unlikely that he does.
Having determined this, the next step is:
So we cannot eliminate row B, because if John was given row B then Peter could have been given columns 3, 6 or 7. Only if he was given column 3 would he know where the treasure is - that's a 33% probability and unlikely to happen in a sense that an even that occurs 66% of the time is more likely to happen than one that occurs only 33% of the time. Right? That is why John says he does not think Peter will know.
The only row we can eliminate is row A. If John was given row A then Peter would have a 50% chance to either know or not know where the treasure is, so John would be unable to say that he doesn't think Peter will know, because with a 50% chance he cannot take a position of what is more likely to happen - Peter knowing or not knowing.
It's a breeze now:
Now Peter says he didn't know where the treasure was, but now he knows. So Peter was not given columns 3 or 5 because then he would know right away. The only way for him to know where the treasure is after only eliminating row A is if the treasure is in F2. Now for John to know where the treasure is after hearing Peter would have to mean that he was given row F and he also deduced that the treasure is in F2.
And that's that.
New contributor
$endgroup$
I have a different answer. It might be a little lateral-thinking, but word choice matters! The treasure is in locker:
F2
The first thing to really pay attention to is when John says:
"I do not think Peter will know".
Why didn't he say I know for a fact Peter does not know? Because he does not know for a fact that Peter does not know. It's like when I go with my friend to play roulette and he puts all his money on 32. I try to talk him out of it by saying "take your money back, I do not think 32 will come up". Why did I say that? Do I know for sure 32 will not come up? Of course not, it's just that it's so unlikely that I do not think it will this time. Same with John, he does not know that Peter for sure does not know where the treasure is, it is just that it is unlikely that he does.
Having determined this, the next step is:
So we cannot eliminate row B, because if John was given row B then Peter could have been given columns 3, 6 or 7. Only if he was given column 3 would he know where the treasure is - that's a 33% probability and unlikely to happen in a sense that an even that occurs 66% of the time is more likely to happen than one that occurs only 33% of the time. Right? That is why John says he does not think Peter will know.
The only row we can eliminate is row A. If John was given row A then Peter would have a 50% chance to either know or not know where the treasure is, so John would be unable to say that he doesn't think Peter will know, because with a 50% chance he cannot take a position of what is more likely to happen - Peter knowing or not knowing.
It's a breeze now:
Now Peter says he didn't know where the treasure was, but now he knows. So Peter was not given columns 3 or 5 because then he would know right away. The only way for him to know where the treasure is after only eliminating row A is if the treasure is in F2. Now for John to know where the treasure is after hearing Peter would have to mean that he was given row F and he also deduced that the treasure is in F2.
And that's that.
New contributor
New contributor
answered 1 hour ago
AmorydaiAmorydai
1565
1565
New contributor
New contributor
add a comment |
add a comment |
Hugo is a new contributor. Be nice, and check out our Code of Conduct.
Hugo is a new contributor. Be nice, and check out our Code of Conduct.
Hugo is a new contributor. Be nice, and check out our Code of Conduct.
Hugo is a new contributor. Be nice, and check out our Code of Conduct.
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%2f79989%2ftreasure-hunt-riddle%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
1
$begingroup$
Do they both have the same list of 10 possible lockers ?
$endgroup$
– Rémi Henry
4 hours ago
$begingroup$
@RémiHenry From my understanding the possible lockers are the ones marked with yellow in the table. Anyway I'm sure they both get the same list of possible lockers.
$endgroup$
– npkllr
4 hours ago
$begingroup$
@npkllr, yes that's what i thought afterward
$endgroup$
– Rémi Henry
4 hours ago
1
$begingroup$
@RémiHenry yes,they both have same list and marked with yellow are the possible lockers.
$endgroup$
– Hugo
4 hours ago