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1 solution
Moderator note:
Good ideas presented. The case of 19 could be better explained, including what the exact pattern is.
The numbers 6, and 11, when squared, cubed, et cetera, always end with a 6, or 1 respectively. 19 however, ends with either a 1 or a 9.
For example:
6 squared = 3 6
1 1 squared = 12 1
1 9 squared = 36 1
1 9 cubed = 685 9
So, if you add 1 + 1 ( 19 to the power of 2016 + 11 to the power of 2016) you get 2. Then you subtract 6, but instead of going into negatives, we add something in the tens column.
12 - 6 = 6
Therefore the number 6 will be in the unit column.