2. Masha wrote one non-zero digit on each of three cards (all digits are different). Dasha formed all possible three-digit numbers from them. Can the sum of these numbers be equal to 2021?
Solution. Let the digits on the cards be $a, b$, and $c$. Since they are all distinct, Dasha formed six numbers. Since each digit appears in the hundreds, tens, and units places twice, their sum is $200(a+b+c)+$ $20(a+b+c)+2(a+b+c)=222(a+b+c)$. Then the equation $222(a+b+c)=2021$ cannot hold, since 222 is divisible by 3, but 2021 is not. Answer: it cannot.