In a sequence {a1,a1,....,an....}
                a1=1 ,
                                           2
        4anan+1=(an+an+1  - 1)
        an+1>an
        Find a1998
 

Question 2:
  Given Hk=[k(k-1)/2]  x  cos[k(k-1)*pi/2]
        Find H19+H20+....+H98

Question 3:

A book has 30 chapters. The lengths of the chapters are 1,2,...30 pages. Chapter One start from page 1 of the book, and
each chapter starts from a new pages. At most how many chapters can start from an odd-numbered page?

Question 4:
On a square carpet of size 123X123, each unit square is colored red or blue. Each red square not lying on the edge of the
carpet has exactly five blue squares among its eight neighbours. Each blue square not lying on the edge of the carpet has
exactly four red squares among its eight neigtbours. Find the numbers of red squares on the carpet.
 

Question 5:
 
In triangle ABC, Angle C=90 degree. Angle A=30 degree and AB=1.
Let Tri ABD, Tri ACE, Tri BCF be equilateral triangle with D,E,F
lying outside Tri ABC. Let DE intersects AB at G. Find the area of Tri DGF.
 

Question 6:
ABCDEF is a regular hexagon, M,N are points on the segments AC, CE respectively such that AM/AC=CN/CE=r. If
B,M,N are collinear, find r.
 

Question 7:
Tri ABC is an equilateral triangle and P is a variable point on the same plane such that Tri PAB, Tri PBC, Tri PCA are
isosceles triangle. In how many different position can P lie?
 

Question 8:
The lengths of the three medians AD, BE and CF of Tri ABC are 9,12,15 respectively. Find the are of Tri ABC.
 

Question 9:
Find the 4-digit number such that, when the order of its digits is reversed, the new value is 4 time the original one.
 

Question 10:
Determine the number of ordered pairs (x,y), where x and y are integers satisfying the equation 2xy-5x+y=55
 

Question 11:
Given that [x] represents the greatest integer not exceeding x, find the last three digits of the integers [1099/(1033+3)]
 

Question 12: 
Let x0=5 and xn+1=xn+1/xn for n=0,1,2,3,4..... Find the integer closest to x1998.
 

Question 13:
At least how many of the + sign in the expression :
     +1+2+3+4....+100
    should be replaced by - signs so that the value is 1998 .
 

Question 14:
Except for the first two terms, each term of the sequence 1000,x,1000-x,....
is obtained by subtracting the preceding term from the one before that. The last term is the first negative term encountered.
What positive integer x produces a sequence of maximum length?
 

Question 15:
In tri ABC, tanA:tanB:tanC=1:2:3 Find AC/AB
 

Question 16:
                                                                                n                             1998
Find the smallest positive integer n such that 1997  -1 is divisible by 2
 

Question 17:
In how many ways can 1998 be expressed as the sum of one or more consecutive integers.
 

Question 18:
What is the largest integer k such that 1001x1002x....x1998/11k is an integer.
 

Question 19:
Find the smallest multiple of 84 whose digits consist entirely of 6's and 7's only.
 

Question 20:
An mxnxp rectangular box has half the volume of an (m+2)x(n+2)x(p+2) rectangular box, where m,n,p are integers and
mnp. What is the largest possible value of p?
 

                                            -End of Paper-