Mixing
I'm a celeb get me outta here: optimal strategy to open locks
$begingroup$
Suppose there are two 4 digit locks and a given and finite set $A$ of 4 digit tuples. Two elements of $A$ open the locks. What shall I do? Stick to the number or stick to the lock?
I. Choose the first element of $A$ and try the locks, then choose the second element of $A$ and try the locks and so forth until both are open.
II. Choose the first lock and try the elements of $A$ until open and then try the remaining elements of $A$ for the second lock.
Edit: The two 4 digit tuples that open the respective locks are distinct. One cannot try to open the locks simultaneously. A strategy is called optimal if it minimizes the attempts to open both locks.
probability recreational-mathematics
asked Jan 19 at 0:22
cluelessclueless
298111
$endgroup$
|
show 3 more comments
$begingroup$
Suppose there are two 4 digit locks and a given and finite set $A$ of 4 digit tuples. Two elements of $A$ open the locks. What shall I do? Stick to the number or stick to the lock?
I. Choose the first element of $A$ and try the locks, then choose the second element of $A$ and try the locks and so forth until both are open.
II. Choose the first lock and try the elements of $A$ until open and then try the remaining elements of $A$ for the second lock.
Edit: The two 4 digit tuples that open the respective locks are distinct. One cannot try to open the locks simultaneously. A strategy is called optimal if it minimizes the attempts to open both locks.
probability recreational-mathematics
asked Jan 19 at 0:22
cluelessclueless
298111
$endgroup$
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
1
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34
|
show 3 more comments
$begingroup$
Suppose there are two 4 digit locks and a given and finite set $A$ of 4 digit tuples. Two elements of $A$ open the locks. What shall I do? Stick to the number or stick to the lock?
I. Choose the first element of $A$ and try the locks, then choose the second element of $A$ and try the locks and so forth until both are open.
II. Choose the first lock and try the elements of $A$ until open and then try the remaining elements of $A$ for the second lock.
Edit: The two 4 digit tuples that open the respective locks are distinct. One cannot try to open the locks simultaneously. A strategy is called optimal if it minimizes the attempts to open both locks.
probability recreational-mathematics
asked Jan 19 at 0:22
cluelessclueless
298111
$endgroup$
Suppose there are two 4 digit locks and a given and finite set $A$ of 4 digit tuples. Two elements of $A$ open the locks. What shall I do? Stick to the number or stick to the lock?
I. Choose the first element of $A$ and try the locks, then choose the second element of $A$ and try the locks and so forth until both are open.
II. Choose the first lock and try the elements of $A$ until open and then try the remaining elements of $A$ for the second lock.
Edit: The two 4 digit tuples that open the respective locks are distinct. One cannot try to open the locks simultaneously. A strategy is called optimal if it minimizes the attempts to open both locks.
probability recreational-mathematics
probability recreational-mathematics
asked Jan 19 at 0:22
cluelessclueless
298111
asked Jan 19 at 0:22
cluelessclueless
298111
edited Jan 19 at 8:53
clueless
asked Jan 19 at 0:22
cluelessclueless
298111
asked Jan 19 at 0:22
cluelessclueless
298111
asked Jan 19 at 0:22
cluelessclueless
298111
298111
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
1
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34
|
show 3 more comments
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
1
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
1
1
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34
|
show 3 more comments
0
active
oldest
votes
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: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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%2fmath.stackexchange.com%2fquestions%2f3078903%2fim-a-celeb-get-me-outta-here-optimal-strategy-to-open-locks%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f3078903%2fim-a-celeb-get-me-outta-here-optimal-strategy-to-open-locks%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
$begingroup$
What have you done so far?
$endgroup$
– saulspatz
Jan 19 at 0:40
$begingroup$
Provide two distinct strategies. I wouldn' t know how to prove that one is optimal. I suppose that it also depends on the cardinality of $A$. Just saw the show and was wondering how to approach the problem.
$endgroup$
– clueless
Jan 19 at 0:57
$begingroup$
Please clarify "Two elements of A open the locks.". Are there precisely two distinct elements of $A$ that open the locks? Do they both open both locks, or one each?
$endgroup$
– Servaes
Jan 19 at 1:10
1
$begingroup$
The two 4 digit tuples that open the locks are distinct and one tuple belongs to one lock each.
$endgroup$
– clueless
Jan 19 at 1:18
$begingroup$
OK great. Next; what do you mean by optimal?
$endgroup$
– Servaes
Jan 19 at 1:34