Question 217724
 palindrome is a number that reads the same forwards and backwards.
 The sum of a particular set of three consecutive positive integers is a three-digit palindrome. 
If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?
:
Less than 220 therefore the number is 212 or the 1st and 3rd digit = 1
I tried 212, does not have an integer solution.

Let the 1st and 3rd digit = 1
Let the middle digit = x
Let consecutive integers = y, y+1, y+2
:
y + (y+1) + (y+2) = 100 + 10x + 1
;
combine like terms
3y + 3 = 10x + 101
;
3y = 10x + 101 - 3
;
3y = 10x + 98
y = {{{(10x+98)/3}}}
:
Find a value for x that will give an integer value for y
The sum of the numerator has to be a multiply of 3
x = 7
y = {{{(10(7)+98)/3}}}
y = {{{(168)/3}}}
y = 56
:
Try this
56 + 57 + 58 = 171, satisfies the problem