proof by letters with characters
$begingroup$
An authentication system accepts passwords that are composed of lowercase letters from a to z and digits from 0 to 9. Prove that, in this system, given any set of 3000 passwords, there must be at least three passwords that begin with the same pair of characters (in the same order), for example, st4fk7 and std3gy37.
combinatorics pigeonhole-principle
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
$endgroup$
add a comment |
$begingroup$
An authentication system accepts passwords that are composed of lowercase letters from a to z and digits from 0 to 9. Prove that, in this system, given any set of 3000 passwords, there must be at least three passwords that begin with the same pair of characters (in the same order), for example, st4fk7 and std3gy37.
combinatorics pigeonhole-principle
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
$endgroup$
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35
add a comment |
$begingroup$
An authentication system accepts passwords that are composed of lowercase letters from a to z and digits from 0 to 9. Prove that, in this system, given any set of 3000 passwords, there must be at least three passwords that begin with the same pair of characters (in the same order), for example, st4fk7 and std3gy37.
combinatorics pigeonhole-principle
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
$endgroup$
An authentication system accepts passwords that are composed of lowercase letters from a to z and digits from 0 to 9. Prove that, in this system, given any set of 3000 passwords, there must be at least three passwords that begin with the same pair of characters (in the same order), for example, st4fk7 and std3gy37.
combinatorics pigeonhole-principle
combinatorics pigeonhole-principle
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
edited Jan 7 at 10:33
N. F. Taussig
44.2k93356
44.2k93356
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
42
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35
add a comment |
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
$endgroup$
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: "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%2f3064137%2fproof-by-letters-with-characters%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
$begingroup$
Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
$endgroup$
add a comment |
$begingroup$
Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
$endgroup$
add a comment |
$begingroup$
Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
$endgroup$
Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
173k7113326
173k7113326
add a comment |
add a comment |
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%2f3064137%2fproof-by-letters-with-characters%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
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to explain what you know, show what you have attempted, and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 7 at 10:35