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# Question

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Determine the number of palindromes with 7 digits.

Apr 22, 2018

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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

There are 900 palindromes with 5 digits

So 1 digit: 9

2 digits: 9

3 digits: 90

4 digits: 90

5 digits: 900

6 digits: 900

7 digits: 9000

9000

Method 2: Counting

The 7 digit palindrome is in this format:

ABCDCBA

There are 9 choices for A

10 for B

10 for C

10 for D

$$9\cdot{10}\cdot{10}\cdot{10}=\boxed{9000}$$

I hope this helped,

Gavin

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Apr 22, 2018
edited by GYanggg  Apr 22, 2018