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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.










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    – N. F. Taussig
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$begingroup$


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.










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    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.
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    – N. F. Taussig
    Jan 7 at 10:35














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$begingroup$


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.










share|cite|improve this question











$endgroup$




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






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edited Jan 7 at 10:33









N. F. Taussig

44.2k93356




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asked Jan 6 at 17:20









Ferda TaşFerda Taş

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42












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    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




$begingroup$
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










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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.






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    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.






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      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.






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        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.






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        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.







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        answered Jan 7 at 11:57









        Christian BlatterChristian Blatter

        173k7113326




        173k7113326






























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