9.1 A stock market player doubles his capital every working day (from Monday to Friday inclusive). But on Saturday and Sunday, he parties, and for each party day, he spends $75\%$ of his wealth. By the evening of December 31, he became a millionaire for the first time in his life. On which day of the week did September 1 of the same year fall - the day he first started trading on the stock market? Justify your answer.
Solution. The trader's capital decreases by a factor of 4 each weekend day, meaning it decreases by a factor of 16 over Saturday and Sunday. Over the next 4 days, by Thursday evening, it can only recover. Therefore, an increase in capital (compared to the previous week) is only possible on Friday. This means that December 31 was a Friday. Therefore, the following days were also Fridays: in December: 24, 17, 10, 3. In November: 26, 19, 12, 5. In October: 29, 22, 15, 8, 1. In September: 24, 17, 10, 3. Thus, September 1 was a Wednesday.

Answer: Wednesday.

| IS IN THE SOLUTION | SCORE |
| :--- | :---: |
| Correct and justified answer | 7 points |
| Proven that December 31 fell on a Friday | 5 points |
| The problem is correctly solved under the assumption that December 31 is a Friday, but this key fact is not justified | 3 points |
| Proven that September 1 could have been a Wednesday (a possible example of capital movement is constructed), but it is not justified that other days of the week do not satisfy the problem's condition | 2 points |
| Correct answer without justification or with incorrect justification | 0 points |