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Find the total number of four-digit palindromes. (Recall that a palindrome is a nonnegative sequence of digits which reads the same forwards and backwards, such as 1331. Zero cannot be the first digit.)

 May 13, 2018
edited by Guest  May 13, 2018
 #1
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There are two methods to do this problem.

 

Method 1: Pattern Finding

 

There are 9 palindromes with 2 digits 

There are 90 palindromes with 3 digits

There are 90 palindromes with 4 digits

 

Method 2: Counting

 

The 4 digit palindrome is in this format:

 

ABBA

 

There are 9 choices for A

10 for B

 

9*10=90

 

I hope this helped, 

 

Gavin

 May 13, 2018

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