Question

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

Answer 1

Answer: 50

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Step-by-step explanation:

We have something in the form ABCD, where A,B,C and D represent the 4 digits of this four-digit number.

Example: A = 1, B = 7, C = 5, D = 9 leads to ABCD = 1759. We aren't multiplying the values.

Since we want a palindrome, this means that

A = D

B = C

So we go from ABCD to ABBA. The A must be an odd number so that ABBA overall is odd. A number is even if its last digit, or units digit, is even.

This restricts our list of choices for A to 5 choices since the list of odd single digit numbers is {1,3,5,7,9}

We can pick any single digit number we want for B, as it wont affect ABBA being even or odd. There are 10 choices for B since there are 10 numbers in this list {0,1,2,3,4,5,6,7,8,9}

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There are 5 choices for A and 10 choices for B, so 5*10 = 50 different numbers in the form ABBA.

Note: We dont have to worry about a leading zero digit, or a zero on the very left side, because A is always odd.

Answer 2

50.

Step-by-step explanation:

4 digit palindromes where the first and last number is 1 must be where the middle 2 numbers are 00 to 99, so this is 10.

There are also 10 of each of the numbers which start and end with 3,5,7 and 9 which is a total of 40.

The answer is 50.