sonnet-twodates

gistfile1.txt

<USER>
### 1. Two Dates
Mateusz has 12 cards with digits:
`0 0 1 1 2 2 3 3 4 4 5 5`
and he arranges them to form dates. The first date of 2025 that he can create using two cards to form the day number, two other cards to form the month number, and four other cards to form the year number will be January 13:
`1 3 0 1 2 0 2 5`
**What will be the last date in 2025 that Mateusz can create using eight of these twelve cards?**

<ASSISTANT>
Let me solve this step by step.

1) First, let me identify the constraints from the problem:
   - Mateusz has cards: 0 0 1 1 2 2 3 3 4 4 5 5
   - Must use exactly 8 cards to form a date: DD MM YYYY
   - Date must be in 2025
   - Looking for the latest possible date

2) For a valid date in 2025:
   - Day must be 01-31 (depending on month)
   - Month must be 01-12
   - Year must be 2025 (fixed)

3) For year 2025:
   - Need 2, 0, 2, 5
   - This uses one '2', one '0', and one '5'

4) After using these cards for the year, remaining cards are:
   - 0, 1, 1, 2, 3, 3, 4, 4, 5

5) For the latest possible date:
   - Want the highest possible month ≤ 12
   - Within that month, want the highest possible day

6) With remaining digits, highest possible month is 12
   - Uses 1, 2

7) After using month digits, remaining cards are:
   - 0, 1, 3, 3, 4, 4, 5

8) For highest valid day in December (month 12):
   - December has 31 days
   - From remaining digits, highest possible valid day is 31
   - Uses 3, 1

Therefore, the last possible date is December 31, 2025:
`3 1 1 2 2 0 2 5`

The answer is December 31, 2025.