Question

Let s be the set of all 4-digit base 10 palindromes, and let t = {a1, a2, a3, ...a10} be a 10-element subset of s. what is the maximum possible value of gcd(a1, a2, a3, ..., a10)?

Answer 1

To find the maximum possible value of gcd(a1, a2, a3, ..., a10), we need to consider the possible values of the palindromes in set t. A 4-digit palindrome has the form ABBA, where A and B represent digits between 0 and 9. The maximum possible value of gcd(a1, a2, a3, ..., a10) is 9.

Step-by-step explanation:

To find the maximum possible value of gcd(a1, a2, a3, ..., a10), we need to consider the possible values of the palindromes in set t. A 4-digit palindrome has the form ABBA, where A and B represent digits between 0 and 9. The greatest common divisor (gcd) of any two palindromes will be equal to the greatest common divisor of their corresponding digits. Since A and B can take any value between 0 and 9, the maximum possible value of gcd(a1, a2, a3, ..., a10) is 9.