2 [ Decimal numeral system ]

A girl replaced each letter in her name with its number in the Russian alphabet. The result was the number 2011533. What is her name?
Note: The first letter has a number either 2 or 20.

## Solution

The number 2011533 needs to be split into single-digit and two-digit numbers so that the corresponding sequence of letters forms a name. The first number cannot be 2, because then the second number would be 0 or 01, which is impossible. Therefore, the first number is 20, i.e., the first letter is "T". The last number is 33, because otherwise the last two numbers would be 53 and 3 or 3 and 3, but there is no 53rd letter in the alphabet, and a girl's name cannot end with "vv". Therefore, the last letter is "y". For the middle letters, the remaining combination is 115, i.e., either $1,1,5$, or 11,5, or 1,15. This corresponds to the sets of letters "aad", "id", and "an". From this, it is clear that the girl's name is Tanya.

## Answer

The girl's name is Tanya.