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
45.1k103358
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
45.1k103358
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
45.1k103358
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
45.1k103358
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
edited Jan 7 at 10:33
N. F. Taussig
45.1k103358
asked Jan 6 at 17:20
Ferda TaşFerda Taş
42
edited Jan 7 at 10:33
N. F. Taussig
45.1k103358
edited Jan 7 at 10:33
N. F. Taussig
45.1k103358
edited Jan 7 at 10:33
N. F. Taussig
45.1k103358
45.1k103358
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
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$begingroup$
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
176k8115328
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1 Answer
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$begingroup$
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
176k8115328
$endgroup$
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
176k8115328
$endgroup$
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
176k8115328
$endgroup$
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
176k8115328
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
176k8115328
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
176k8115328
answered Jan 7 at 11:57
Christian BlatterChristian Blatter
176k8115328
176k8115328
add a comment |
add a comment |
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$begingroup$
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