A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321 is a palindrome.) Let N be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of N?

Work Shown:

Let a,b,c be three different two-digit palindromes

So N = a+b+c is the sum of those values

The two digit palindromes are {11,22,33,44,55,66,77,88,99} which will represent the possible values of a,b,c.

Let's pick the three smallest values and add them up

11+22+33 = 66

The result isn't three digits, so let's erase 11 and pick 44 this time

22+33+44 = 99

which also isn't three digits. Bump off the smallest value and pick the next largest two digit palindrome, add them up to get

33+44+55 = 132

This sum is now three digits and it's also not a palindrome

The sum of the digits of 132 is 1+3+2 = 6 which is the answer.

So in short, the plan to solve this is to pick the smallest items in the set

{11,22,33,44,55,66,77,88,99}

and use trial and error to see which items add to a three digit non-palindromic number. We picked the smallest items to ensure that N is the smallest three digit number.

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.

step-by-step :