
Exercises and problems in Informatics January 2003 
I. 40. Every row, column and both main
diagonals of the square in the figure contain a prime number
with five digits when rows and the diagonals are read from left to
right, and columns from top to bottom. Moreover,
the sum of the digits of the prime numbers must be the same,
the digit in the top left corner is given in advance,
any prime number can be reused in the actual square and
a prime number can not have any zero leading digit, that is,
for example, 00003 is not a prime number with five digits.
1  1  3  5  1  3  3  2  0  3  3  0  3  2  3  1  4  0  3  3  3  3  3  1  1 

Your program (I40.pas, ...) should read the sum of
the digits of the prime numbers, further the digit to be placed into
the top left corner, then display the corresponding square.
In the example, the sum of the digits=11,
while the top left digit=1.
(10 points)
I. 41. A square is divided into smaller
light or dark squares. We can obtain different figures by rotating the
original square or reflecting it around its axes of
symmetry. (However, it may happen that some transformations, or
combination of transformations produce the same  possibly the
original  figure.)
Write your program (I41.pas, ...) which reads the
colouring of the NxN square using the symbols V
(=light) and S (=dark), successively representing in each row
the colours of the small squares, then displays the square together
with all different images under all combinations of
transformations.
The example shows for N=3 the
original square=((S,S,V),(V,V,V),(V,S,S)) and all possible
images under the transformations.
(10 points)
I. 42. The exchange rates between 100 units
of some foreign currency and HUF (=Ft) are stored in a table. For
example, 100 AUD is worth 13279 HUF.
Prepare a sheet (I42.xls) which  using a
fixed table of foreign currency  computes all the exchange rates
in the fourth column if any amount of a single (but arbitrary)
currency in the third column has been entered.
See the examples.
100  HUF  amount  value      AUD  13279   176,96  CAD  15014   156,51  CHF  16287   144,28  CZK  777   3024,32  EUR  23835   98,59  HUF  100   23499,00  PLZ  6051   388,35  SEK  2618   897,59  SKK  580   4051,55  USD  23499  100  100,00 

  100  HUF  amount  value      AUD  13279   2,93  CAD  15014   2,59  CHF  16287   2,39  CZK  777  50  50,00  EUR  23835   1,63  HUF  100   388,50  PLZ  6051   6,42  SEK  2618   14,84  SKK  580   66,98  USD  23499   1,65 


(10 points)
Send your solutions to the following email address:
Deadline: 13 February 2003
