16.(20 12? Chongqing) Party A and Party B play card games and get cards from a sufficient number of cards. It is stipulated that each person can get cards in two ways at most, with Party A taking four or (4k) cards at a time and Party B taking six or (6k) cards at a time (k is a constant, 0 < k < 4). According to statistics, Party A accounts for * *.

Analysis: Suppose A takes (4﹣k) chess pieces and B takes (6﹣k) chess pieces, then A takes (15﹣a) chess pieces and B takes (17﹣b) chess pieces, so that according to

Solution: Let A take (4﹣k) pieces, and B take (6﹣k) pieces, then A takes (15﹣a) pieces and B takes (17﹣b) pieces.

Then Party A takes a (60﹣ka) card and Party B takes a (102﹣kb) card.

Then always * * * get the card: n = a (4 ﹣ k)+4 (15 ﹣ a)+b (6 ﹣ k)+6 (17 ﹣ b) = ﹣.

Therefore, to reduce the number of cards as much as possible, you can reduce N as much as possible, because K is a positive number and the function is a subtraction function, and (a+b) can be made as large as possible.

Judging from the meaning of the question, a≤ 15, b≤ 16,

The total number of cards held by the last two people is exactly the same.

Therefore, k (b-a) = 42, and when 0 < k < 4, b-a is an integer.

Then k can be 1, 2, 3,

(1) When k= 1 and B-A = 42, this situation is omitted because a≤ 15 and b≤ 16;

(2) When k=2, b﹣a=2 1, which is omitted because a≤ 15 and b≤ 16;

③ When k=3, B-A = 14, which can satisfy the meaning of the question.

To sum up, we can get the following results: a≤ 15, b≤ 16, b﹣a= 14, and (a+b) is the largest.

Then b= 16 and a = 2；; b= 15，a = 1； b= 14，a = 0；

When b= 16 and a=2, a+b is the largest and a+b= 18.

Then k=3, (a+b)= 18,

So n =-3×18+162 =108 sheets.

Comments: This question belongs to the application category. We designed the divisibility of numbers, the increase and decrease of a linear function, and the solution of the maximum value, which is very comprehensive. To solve this problem, we must be familiar with the application of all parts of knowledge in practical problems and think more.