Marta chose a 3-digit number with different non-zero digits and multiplied it by 3. The result was a 3-digit number with all digits equal to the tens digit of the chosen number. What number did Marta choose?

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Solution

Let the chosen number be $a b c$. Then, we have:

| $a b c$ |
| ---: |
| $a b c$ |
| $+\quad b \quad c$ |
| $b b b$ |

Let's analyze case by case: If $c=1$, then $b=3$, which is not possible because the tens digit of the result should be 9; if $c=2$, then $b=6$, which is not possible because the tens digit of the result should be 8; if $c=3$, then $b=9$, which is not possible because the tens digit of the result should be 7; if $c=4$, then $b=2$, which is not possible because the tens digit of the result should be 7; if $c=5$, then $b=5$, which is not possible because the digits must be different; if $c=6$, then $b=8$, which is not possible because the tens digit of the result should be 5; if $c=7$, then $b=1$, which is not possible because the tens digit of the result should be 5; if $c=8$, then $b=4$ and, consequently, $a=1$; if $c=9$, then $b=7$, which is not possible because the tens digit of the result should be 3. Therefore, the number chosen by Marta was 148.