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How many palindromes between 1000 and 9999 are divisible by 5?

User Mirian
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2 Answers

5 votes

Number of digits 5

Range of numbers 10000-99999

Cumulative palindromic numbers 1099

User Thomas
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Answer:

Explanation:

To be divisible by 5, the last digit of the palindrome must be either 0 or 5.

If the last digit is 0, then the first digit must also be 0, since the number is a palindrome. This gives us only one possibility: 1001, which is not divisible by 5.

If the last digit is 5, then the first digit can be any number from 1 to 9, since leading zeros are not allowed. This gives us 9 possible choices for the first digit. For each choice of the first digit, the second digit can be any number from 0 to 9, giving us 10 choices. Thus, there are 9 x 10 = 90 palindromes between 1000 and 9999 that end in 5.

Therefore, there are 90 palindromes between 1000 and 9999 that are divisible by 5.

User Villanuevaquelin
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