2012 correct dice (cubes) are arranged in a row such that every two adjacent dice touch each other with the same faces (domino principle). In all other respects, the position of the dice is random. Find the sum of the points that ended up on the surface of the resulting figure.

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The sum of the points on a die is $1+2+3+4+5+6=21$. The total sum of points on all dice is 2012$\cdot$21. For a fair die, the sum of the points on opposite faces is 7. Let the number of points on the end face of the first die be $x$. Then the number of points on the end face of the last die is also $x$. Therefore, the sum of the points on the adjacent faces is $2012 \cdot 7-2 x$.

Subtracting this sum from the total number of points, we get: $2012 \cdot(21-7)+2 x=28168+2 x$.

## Answer

$28170,28172,28174,28176,28178$ or 28180.