53. How old is Sofia Sergeyevna? Our acquaintance Sofia Sergeyevna is not old, as she was born after World War I, but she does not like to answer directly when asked how old she is.

When asked on July 27, 1950, how old she was, she replied: I am only one year old, because I only celebrate my birthday when it falls on the same day of the week as the day I was born, and I have only celebrated such a birthday once.

How old is Sofia Sergeyevna?
53. Let's denote the days of the week as I, II, ..., VII and construct a table, agreeing that the day of the week that fell on a certain specific date in 1911 is denoted by the number I.

| $\boldsymbol{A}$ | B | c | $D$ | $A$ | $B$ | $c$ | D |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1911 | I | I |  | 1931 | v | $\mathbf{V}$ |  |
| 1912 | II | III | I | 1932 | VI | VII | V |
| 1913 | IV | IV |  | 1933 | I | I |  |
| 1914 | $\mathrm{~V}$ | $\mathrm{~V}$ |  | 1934 | II | II |  |
| 1915 | VI | VI |  | 1935 | III | III |  |
| 1916 | VII | I | VI | 1936 | IV | $\mathrm{V}$ | III |
| 1917 | II | II |  | 1937 | VI | VI |  |
| 1918 | III | III |  | 1938 | VII | VII |  |
| 1919 | IV | IV |  | 1939 | I | I |  |
| 1920 | V | VI | IV | 1940 | II | III | I |
| 1921 | VII | VII |  | 1941 | IV | IV |  |
| 1922 | I | I |  | 1942 | $\mathrm{~V}$ | $\mathrm{v}$ |  |
| 1923 | II | II |  | 1943 | VI | VI |  |
| 1924 | III | IV | II | 1944 | VII | I | VI |
| 1925 | $\mathrm{~V}$ | $\mathrm{~V}$ |  | 1945 | II | II |  |
| 1926 | VI | VI |  | 1946 | III | III |  |
| 1927 | VII | VII |  | 1947 | IV | IV |  |
| 1928 | I | II | VII | 1948 | $\mathrm{~V}$ | VI | IV |
| 1929 | III | III |  | 1949 | VII | VII |  |
| 1930 | IV | IV |  | 1950 | I | I |  |

In column $A$, the years are listed (leap years are printed in bold). In column $B$, the days of the week are listed that fall on the same date as in 1911, if this date is between January 1 and February 28. In column $C$, the days of the week are listed that fall on the same date as in 1911, if this date is between March 1 and December 31. In column $D$, the days of the week are listed that fall on February 29 in certain leap years.

From this table, it is clear that the day of the week that falls on a certain date before March 1 moves forward by 1 after a common year, and by 2 after a leap year; the day of the week that falls on a certain date after March 1 moves forward by 1 before a common year, and by 2 before a leap year.

From this table, it is also clear that if a certain date (other than February 29) falls on, for example, a Monday in a certain year, then it will fall on the same day of the week again either after 5 years, or after 6 years, or after 11 years (if the period under consideration does not include a year whose number is divisible by 100 but not by 400).

If Sofia Sergeyevna were born on any day other than February 29, and by July 27, 1950, she had celebrated her birthday only once, then she would still be a minor, and there would be no reason to call her Sofia Sergeyevna or to say that she is not old.

Therefore, let's assume that Sofia Sergeyevna was born on February 29. The day of the week that falls on this date moves forward by 5 every four years, as a result, February 29 falls on the same day of the week every $7 \cdot 4=28$ years (if the period does not include a year whose number is divisible by 100 but not by 400). Since Sofia Sergeyevna is "only one year old," she celebrated her first birthday as early as 1924 and as late as 1948.

But since it is known that Sofia Sergeyevna was born after World War I, she celebrated her first birthday in 1948 and was born on February 29, 1920.