6.3. Find all solutions to the puzzle: ТУК + ТУК + ТУК + ТУК + ТУК = СТУК. The same letters correspond to the same digits, different letters correspond to different digits.
Answer. Two solutions $(250+\ldots+250=1250$ and $750+\ldots+750=3750)$.

Solution. Subtract TUK from both sides of the equation. We get: TUK + TUK + TUK + $T U K=C 000$. That is, $4 \cdot T U K=C \cdot 1000$. Dividing by 4, we get: $T U K=C \cdot 250$. The number $T U K-$ is a three-digit number, so $C<4$. Checking shows that the digits $C=1$, then $T U K=250$ and $C=$ 3, then $T U K=750$ fit, while the digit $C=2$, does not fit - then $T U K=500-$ has identical digits.

Comment. Just the correct answer - 3 points;

One of the two correct answers - 1 point.

The guess of subtracting the number $T U K$ from both sides is present - 2 points.