Question 909151
Easiest way for me is estimation.
Possibles (because of the first constraint) are 14,25,36,47,58,69
Let's start with one in the middle: 36
{{{3^3}}}=9; {{{6^2}}}=36; difference of 25 and 36 =11
{{{2^2}}}=4; {{{5^5}}}=25; difference of 21 and 25 = 4
{{{1^2}}}=1; {{{4^2}}}=16; difference of 15 and 14 = 1
Hmmm...
{{{6^2}}}=36;{{{9^2}}}=81; difference of 45 and 69 = 24
{{{5^2}}}=25; {{{8^2}}}=64; difference of 39 and 58 = 19 
{{{4^4}}}=16; {{{7^2}}}=49; difference of 33 and 47 = 14 
Unless I've miscalculated somewhere, there is no solution where the difference ends up to be 12.