## Exercises and problems in Informatics |

## Please read The Conditions of the Problem Solving Competition.

**I. 73.** Write a program (i73.pas, ...) that determines all prime numbers having *N* digits with the property that their digits in any order yield another prime number with *N* digits. The program should display all these primes together with all possible permutations of their digits, but should not display any prime that has already been printed as a permutation of another one.
(*10 points*)

**I. 74.** Newton studied the following curves described by the equation

*y*^{2}=*x*(*x*^{2}+*ax*+*b*).

Write your program (i74.pas) which plots the above
curve for any given *a* and *b*. The *example*
shows the curve corresponding to *a*=1, *b*=0; *a*=0,
*b*=-1; *a*=0, *b*=1, respectively.

(*10 points*)

**I. 75.** The *B*(*n*,*k*)
binomial coefficients in Pascal's triangle can be generalized to
negative integer values of *n* using Pascal's addition formula
(that is each element is obtained by adding its upper and upper left
neighbours). Prepare your sheet (i75.xls) that computes the negative
extension of Pascal's triangle from *B*(0,0) to
*B*(-*n*,*n*), if *n* is given.

The table shows an example for *n*=6.

-6 | 1 | -6 | 21 | -56 | 126 | -252 |

-5 | 1 | -5 | 15 | -35 | 70 | -126 |

-4 | 1 | -4 | 10 | -20 | 35 | -56 |

-3 | 1 | -3 | 6 | -10 | 15 | -21 |

-2 | 1 | -2 | 3 | -4 | 5 | -6 |

-1 | 1 | -1 | 1 | -1 | 1 | -1 |

0 | 1 | 0 | 0 | 0 | 0 | 0 |

(*10 points*)