The British Informatics Olympiad is the computing competition for schools and colleges. We are proud to present BIO 2000. 
The 2000 British Informatics Olympiad  Round One
Time allowed: 3 hours
Instructions
You should write a program for part (a) of each question, and produce written answers to the remaining parts. The written questions can be solved without writing the program for part (a), although you may write a program to help produce these answers if you wish.
You may use a calculator and the online help that your programming language provides, and you should have a pen, some blank paper, and a blank floppy disk on which to save your programs. You must not use any other material such as disks, files on a computer network, books or other written information.
Mark the first page used for your written answers with your name, age in years and school/college. Number all pages in order if you use more than one sheet. All of your computer programs should display your name and school/college when they are run, and the floppy disk you use to submit the programs should also show your name and school/college.
For your programs to be marked, the source code must be saved, along with executables if your language includes a compiler. This includes programs used to help answer written questions. You must clearly indicate the name given to each program on your answer sheet(s).
Sample runs are given for parts 1(a), 2(a) and 3(a). Bold text indicates output from the program, and normal text shows data that has been entered. The output format of your programs should follow the 'sample run' examples. Your programs should take less than two minutes of processing time for each test.
Attempt as many questions as you can. Marks allocated to each part are shown in square brackets next to the questions. Partial solutions (such as programs that only satisfy some of the specified requirements, or partly completed written answers) may get partial marks. Questions can be answered in any order.
Question 1 Passwords 
Some computer programs try to prevent easily guessable passwords being used, by rejecting those that do not meet some simple rules. One simple rule is to reject passwords which contain any sequence of letters immediately followed by the same sequence.
For example:
APPLE Rejected (P is repeated) CUCUMBER Rejected (CU is repeated) ONION Accepted (ON is not immediately repeated) APRICOT Accepted 

1 (a) [22 marks] 
Write a program which inputs a password (between 1 and 10 upper case letters) and then prints Rejected if the password is rejected, or Accepted otherwise. Your program should then terminate.  Sample run Password: BANANA Rejected 
1 (b) [5 marks] 
Suppose the only valid letters are A and B; the password ABA cannot be made longer since both ABAA and ABAB will be rejected. What is the length of the shortest password that cannot be made longer, if A, B and C are valid? Give an example. 
Question 2 Ants 
Two ants are crawling over a virtual landscape, changing the scenery as they move. Your task in this question is to model their behaviour.
The landscape is an 11 by 11 grid. The bottom left square is at (1,1) and the xaxis runs along the bottom of the grid. Each square is coloured either black or white. A square can contain either, both or neither of the ants. Each ant wanders around the grid in a set way. An ant moves one square forward in the direction it is facing. If the square it lands on is black it rotates 90° left, if it is white it rotates 90° right. The colour of the square it is on is then changed. An ant that moves off the edge of the board is removed from the simulation. For example: 
In each move of the simulation, the ants move in turn as follows. First, ant 1 moves as described above. Once its final step is complete, i.e. once it has changed the colour of the square it landed on, ant 2 moves. 
2 (a) [30 marks] 
Write an interactive program to model the behaviour of the ants. Your program should first read in two lines, describing the starting position of ants 1 and 2 respectively. Each line will contain two numbers, the x coordinate then the y coordinate of the ant, followed by a letter indicating the direction the ant is facing. The letter, 'T', 'B', 'L' or 'R', indicates the top, bottom, left or right of the grid.
The landscape starts off with every square white. Until your program terminates you should repeatedly wait for input and then:

Sample run 5 5 T 3 9 B 6 ........... ........... .**........ .*.*....... ........... ...*.*..... ....**..... ........... ........... ........... ........... 4 6 T 4 8 B 1 ........... ........... .**........ .*.*....... ........... ...*.*..... ....**..... ........... ........... ........... ........... 4 7 R 4 7 R 59 ...**...... ..****..... .*.**.*.... *...***.... .*...*..... *.*..*..... .*...*..... .*...*..... ..*..*..... ...**...... ........... 6 4 B Removed 1 
2 (b) [5 marks] 
What did the landscape shown on the left look
like 6 moves earlier?
[Draw the landscape, and write the coordinates and directions for the two ants using the same notation as for question 2(a).] 
2 (c) [5 marks] 
At the start of the simulation Ant 1 is facing left. Much later in the simulation there is an ant on the same square facing top. Can it be the same ant? Justify your answer. 
Question 3 Playing games note: 'die' is the singular of 'dice' 
Romulus and Remus are playing a game where they take it in turns to throw a pair of dice and then add the two numbers. In order to make the game fair, the possible scores from Romulus' pair of dice and Remus' dice, and the number of different ways each of them can be formed, must be the same. Every side of a die consists of a single positive integer. [NB: This excludes 0.]
For example, Romulus has a normal pair of six sided dice (each numbered {1,2,3,4,5,6}) and Remus has an unusual pair of dice: the first numbered {1,2,2,3,3,4}, and the second numbered {1,3,4,5,6,8}. This is fair because both pairs of dice can make the numbers from 2 to 12, and (for example) 6 can be made in 5 ways with each pair. 
3 (a) [20 marks] 
Write a program that inputs the values on one of the pairs of dice and then outputs a different pair of dice that could be used to play a fair game. Two dice are only different if they have different sides; so {1,2,3,4,5,6} and {6,5,4,3,2,1} are not different. Similarly, a different order does not distinguish two pairs of dice; so {1,2,3} and {4,5,6} is not different to {4,5,6} and {1,2,3}.
The first line of input will consist of a single integer 'n' (1 <= n <= 8) denoting the number of sides all the dice will have. The second line will consist of 'n' integers (in the range 1 to 8) giving the values on the sides of the first die. The third line will also consist of 'n' integers (in the range 1 to 8) giving the values for the second die. Your output should consist of an example solution if you believe there to be one (with one die given on each line), or the word Impossible if you do not. Note that the example solution does not need to be sorted, and the value on a side can be any positive integer (i.e. values may be greater than 8). 
Sample run 6 2 4 1 3 5 6 6 4 2 3 1 5 1 2 2 3 3 4 8 6 5 4 3 1 
3 (b) [4 marks] 
Three equivalent pairs of dice have been mixed together. The six dice are labelled {1,5,6,7,9,10}, {2,3,4,6,7,8}, {2,6,7,8,10,11}, {1,2,3,5,6,7}, {3,7,8,9,11,12} and {3,4,5,7,8,9}. What were the original pairings? 
3 (c) [4 marks] 
Given two 'n' sided dice, what is the largest number of distinct sums that can be formed? What is the smallest? 
Total marks: 100.
End of BIO 2000 Round One paper