COMP9021 Assignment 1 Solution

1. General matters
1.1. Aims. The purpose of the assignment is to:
• let you design solutions to simple problems;
• let you implement these solutions in the form of short python programs;
• practice the use of arithmetic computations, tests, repetitions, lists, tuples, dictionnaries.
Your program should not make any assumption on the actual solution, except obvious ones on the ranges of some values. Hard coded solutions (that is, programs that more or less just print out the solution) will not receive any mark.
The outputs of your programs should be exactly as indicated.
1
2. An equation
Write a python program, named equation.py, that solves the equation
abc ∗ de ∗ fg = a∗ bc ∗ defg
where each of the letters a to g stands for a nonzero digit, and where different letters possibly stand for the same digit. For instance, if we make a = 2, b = 7, c = 5, d = 6, e = 6, f = 5, and g = 5, then the equation reads
275 ∗ 66 ∗ 55 = 2 ∗ 75 ∗ 6655
which happens to be true, making this specific assignment of digits to the letters a to g a particular solution.
The output of your program should be of the form:
There are X solutions :
∗ ∗ = ∗ ∗

of course replacing X by the appropriate number and then displaying all solutions as shown, of course replacing every occurrence of _ by an appropriate digit, one solution per line, in lexicographic order (so from the lowest values of abc to the largest values of abc, and for a given value of abc from the lowest values of de to the largest values of de, etc.).
3
3. A multiple of 2004
Write a python program, named multiple_2004.py, that finds two strictly positive integers A and B so that A2004B (the digits in A followed by 2004 followed by the digits in B) is the smallest multiple of 2004 possible.
The output of your program should be of the form:
A = , B = , N = is the solution .
of course replacing each occurrence of _ by the appropriate number.
4. A grid of numbers
Write a python program, named adjacency_grid.py, that arranges the numbers 1 to 8 in the grid below such that adjacent numbers are not in adjacent cells (neither horizontally nor vertically nor diagonally).

For instance,
1
6 4 3
2 7 5
8
is not a solution because of 3 being adjacent to 4, and 4 being adjacent to 5, and 6 being adjacent to 7, and 7 being adjacent to 8. The output of your program should be of the form

. . .
of course replacing each occurrence of _ by the appropriate digit, consecutive solutions being separated by a blank line (but with no blank line before of after the last solution), in lexicographic order (reading the values in the grid from top to bottom and from left to right).
You might find it useful to make use of the following statement:
from itertools import permutations
5
5. A division
Write a python program, named division.py, that solves the division below where a as well as every star stands for a digit. Different stars can stand for the same digit. All occurrences of a stand for the same digit, and no star stands for that digit. Of course, no number starts with 0.
* * * * a * * | * a *
|--------
* * a a | * * a *
------- |
* * * a |
* * a |
----- |
* * * * |
* a * * |
------- |
* * * * |
* * * * |
------- |
0 |
There is a actually a unique solution. The output of your program should be of the form
/ = is the solution .
of course replacing each occurrence of _ by the appropriate digit.
6. A pivoting die
Consider the board below, which can be imagined as being infinite, so only a small part is represented. A die is placed on cell number 1 of the board in the position indicated: 3 at the top, 2 at the front (towards cell number 4 of the board), and 1 on the right (towards cell number 2 of the board). Recall that 4 is opposite to 3, 5 is opposite to 2, and 6 is opposite to 1. The die can be moved from cell 1 to cell 2, then to cell 3, then to cell 4..., each time pivoting by 90 degrees in the appropriate direction (to the right, forwards, to the left, or backwards). For instance, after it has been moved from cell 1 to cell 2, 2 is still at the front but 6 is at the top and 3 is on the right.

43
42
41
40
39
38
37 44 45 46 47 48 49 50
21
20
19
18
17 22 23 24 25 26
27
28
29
30
31
7
6
5 8 9 10
11
12
13
1 2
3
4
16 15 14
36 35 34 33 32

Write a python program, named pivoting_die.py, that prompts the user for a natural number N at least equal to 1, and outputs the numbers at the top, the front and the right after the die has been moved to cell N.
Here is a possible interaction.
$ python pivoting die . py
Enter the desired goal cell number : A
Incorrect value , try again
Enter the desired goal cell number :
Incorrect value , try again
Enter the desired goal cell number : −1
Incorrect value , try again
Enter the desired goal cell number : 0 Incorrect value , try again
Enter the desired goal cell number : 1
On cell 1 , 3 is at the top , 2 at the front , and 1 on the right .
$ python pivoting die . py
Enter the desired goal cell number : 29
On cell 29 , 3 is at the top , 2 at the front , and 1 on the right .
$ python pivoting die . py
Enter the desired goal cell number : 2006
On cell 2006 , 4 is at the top , 1 at the front , and 2 on the right .