Question 7
Anh and Bao are playing a game using the 2025 calendar. First, Anh chooses a date in January. Next, Bao chooses a date later in the calendar year, but he must keep either the month or the day from Anh’s previous move. The game continues in a similar way where they take turns and whoever chooses December 31st is the winner. One example of a played game is shared below, with Bao winning:
| Player | Chosen date |
| --- | --- |
| Anh | January 7th |
| Bao | April 7th |
| Anh | May 7th |
| Bao | May 19th |
| Anh | May 21st |
| Bao | September 21st |
| Anh | November 21st |
| Bao | November 30th |
| Anh | December 30th |
| Bao | December 31st |
If Anh has a winning strategy, which date in January should he choose on the first move?
Answer format: enter the day number in January.
| Player | Chosen date |
| --- | --- |
| Anh | January 7th |
| Bao | April 7th |
| Anh | May 7th |
| Bao | May 19th |
| Anh | May 21st |
| Bao | September 21st |
| Anh | November 21st |
| Bao | November 30th |
| Anh | December 30th |
| Bao | December 31st |
If Anh has a winning strategy, which date in January should he choose on the first move?
Answer format: enter the day number in January.