Divisible Palindrome
What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?
Problem
Palindromic numbers read the same backwards and forwards, e.g. 7227 or 10101.
What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 5775
Multiple of 15 $\Rightarrow$ multiple of 5 so ends in 5 or 0
0 __ __ 0 not 4 digits
5 __ __ 5
5 + __ + __ + 5 a multiple of 3
Largest possible
5 + 9 + 9 + 5 = 28 no
5 + 8 + 8 + 5 = 26 no
5 + 7 + 7 + 5 = 24 yes