Mathematics Master Lecture Series
《The Art of Apportion》
Professor Siu Man Keung
University of Hong Kong
The content of the lecture is summarized in the following file:
《Games in Mathematics》
Professor Ng Kwok Po
Hong Kong Baptist University
Step 1: Choose 1 card from the 21 card.
(In the example: 5 of Spades is the chosen card.)
Step 2: Move the row with the chosen card to the middle.
Step 3: Rearrange the card by the following method.
|
1 |
8 | 15 | 1 | 2 | 3 | |
|
2 |
9 | 16 | 4 | 5 | 6 | |
|
3 |
10 | 17 | 7 | 8 | 9 | |
|
4 |
11 | 18 | => |
10 |
11 |
12 |
| 5 | 12 | 19 | 13 | 14 |
15 |
|
| 6 | 13 | 20 | 16 | 17 |
18 |
|
| 7 | 14 | 21 | 19 | 20 |
21 |
Step 4: Repeat Step 2 and Step 3 twice.
Step 5: The chosen card is now at the middle!
Example:
Challenging Questions:
- If there are 999 x 999 distinct cards, how many rearrangements is required for the chosen card to be at the middle?
- If there are p x q distinct cards, where p and q are odd numbers, how many rearrangements is required for the chosen card to be at the middle?
3. If p or q is even, will the same results happen?
