To solve this, follow these steps:
1. Identify numbers divisible by 4 between 1 and 65. These are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64.
2. Swap the digits in each number:
13 | 2 | - | 4 | 2 | 8 | 3 | 6 |
8 | 21 | 61 | 42 | 4 | 82 | 5 | 26 |
10. Filter only valid two-digit numbers: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64.
11. Sort in ascending order: 2, 4, 12, 14, 16, 20, 24, 28, 32, 34, 36, 38, 40, 44, 46, 48.
12. Arrange and find the 10th to last: 40.
The number at the 10th position from the last is 40.
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: