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Problem of the Week Problem C Palindrome Hunt A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward. The number 9876789 is a seven-digit palindrome. Find all seven-digit palindromes that satisfy each of the following conditions: • four of the digits are different; and • the number is divisible by 45; and • the sum of the digits of the number is equal to 45. The number 9876789 only satisfies the first condition. Divisibility fact: An integer is divisible by 9 if the sum of the digits of the integer is divisible by 9. Strand Number Sense and Numeration