
Exercises and problems in Informatics April 2003 
I. 49. N fans watching a match throw up their caps as their team wins and then every fan catches exactly one cap falling down. Write a program (i49.pas, ...) that displays the number of possible ways of exactly K (0\(\displaystyle \le\)K\(\displaystyle \le\)N) ones out of the N (0\(\displaystyle \le\)N\(\displaystyle \le\)12) fans getting their own caps back.
The example shows all cases for N,K\(\displaystyle \le\)4.
(10 points)
 K=0  K=1  K=2  K=3  K=4  N=0  1      N=1  0  1     N=2  1  0  1    N=3  2  3  0  1   N=4  9  8  6  0  1 

I. 50. We make a wallpaperpattern by first dividing a square into four equal squares, then removing the quarters adjacent to the centre of the original square. These steps are iteratively applied again to the remaining 3 quarters in each smaller square. We repeat the process N times, see the Figures.
Your program (i50.pas, ...) should display the resulting wallpaperpattern if N (1\(\displaystyle \le\)N\(\displaystyle \le\)10) is given.
(10 points)
I. 51. At the beginning of the day on a stock exchange, the current rate of each share is known. During the day we get a list of the actual sales (i.e. which and how many shares are sold as well as their sale prices) arranged in chronological order (at most 1000 sales are recorded). Columns of the first figure show the number of the transaction, the name of the share, the amount sold and the sale price, respectively.
Time  Share  Amount  Price  1  OTP  20  1500  2  OTP  23  1300  3  MALÉV  5  1000  4  OTP  20  1400  5  MOL  80  1000  6  MOL  10  900 

Prepare your sheet (i51.xls) which  using these data  computes for each stock (i.e. columns of the second figure) its final price at the end of the day (second row), the difference (third row) between the starting price (given in the first row) and final price, the amount of stocks sold (fourth row) and the total value of that stock (fifth row). Stocks that were sold at a higher price on the whole compared to their daily starting prices should be marked red, while those at lower prices should be marked blue.
(10 points)
 OTP  MÁV  MALÉV  MOL  Starting price  1342  1443  1443  1111  Final price  1400  1443  1000  900  Difference  58  0  443  211  Amount  63  0  5  90  Total value  87900  0  5000  89000 

Send your solutions to the following email address:
Deadline: 13 May 2003