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?