IOI'94 - Day 1 - Problem 3: The Primes

|---|---|---|---|---|
| 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 |
|---|---|---|---|---|  (Figure 1)

Figure 1 shows a square. Each row, each column and the two diagonals can be read
as a five digit prime number. The rows are read from left to right. The columns
are read from top to bottom. Both diagonals are read from left to right. Using
the data in the INPUT.TXT file, write a program that constructs such
squares.

The prime numbers must have the same digit sum (11 in the example).
The digit in the top left-hand corner of the square is pre-determined (1 in
the example).
A prime number may be used more than once in the same square.
If there are several solutions, all must be presented.
A five digit prime number cannot begin with zeros, ie 00003 is NOT a five
digit prime number.

Input Data

The program reads data from the INPUT.TXT file.
First the digit sum of prime numbers and then the digit in the top left-hand
corner of the square. The file contains two lines. There will always be a
solution to the given test data. In our example:

11
1

Output Data

In the OUTPUT.TXT file, write five lines for each
solution found, where each line in turn consists of a five digit prime number.
The above example has 3 solutions which means that the OUTPUT.TXT
file contains the following (the empty lines are optional):