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The 2018 British Informatics Olympiad
Instructions
You should write a program for part (a) of each question, and produce written answers to the
remaining parts. Programs may be used to help produce the answers to these written questions but
are not always necessary.
You may use a calculator and the on-line help that your programming language provides. You should
have a pen, some blank paper, and an empty USB stick (or other storage device) on which to save
your programs. You must not use any other material such as files on a computer network, books or
other written information. You may not communicate with anyone, other than the person invigilating
this paper.
Mark the first page of 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 storage device 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. Where multiple items of input appear on the
same line they should be separated by a single space. The output format of your programs should
follow the ‘sample run’ examples. Your programs should take less than 1 second of processing time
for each test.
Attempt as many questions as you can. Do not worry if you are unable to finish this paper in the time
available. Marks allocated to each part of a question are shown in square brackets next to the
questions. Partial solutions (such as programs that only get some of the test cases correct within the
time limit, or partly completed written answers) may get partial marks.
Questions can be answered in any order, and you may answer the written questions without
attempting the programming parts.
Hints
- (^) If you can only see how to solve part of a problem it is worth writing a program that solves that part.
We want to give you marks and questions are evaluated using multiple tests of differing difficulty.
Remember, partial solutions may get partial marks.
- (^) Question 2 is an implementation challenge and question 3 is a problem solving challenge.
- (^) Most written questions can be solved by hand without solving the programming parts.
- (^) Do not forget to indicate the name given to your programs on your answer sheet(s).
Question 1: Debt Repayment
At the end of every month interest is added to a debt (initially 100) and then repayments are taken off.
The interest is a fixed percentage of the current debt. The repayment is also a fixed percentage of the
debt (after the interest has been added) or 50, whichever is larger. If the repayment is greater than the
debt it is reduced to match the debt. The cycle of interest and repayment is continued until the debt has
been reduced to 0 and paid off.
For example, suppose the interest is 10% and repayments are 50%:
- At the end of the first month the interest is 10, increasing the debt to 110;
- The repayment is 55 (50% of 110) leaving the debt at 55;
- At the end of the second month the interest is 5.5, increasing the debt to 60.5;
- The repayment is 50 (as 50% of 60.5 is less than the minimum amount), leaving the debt at 10.5;
- At the end of the third month the interest is 1.05, increasing the debt to 11.55;
- The repayment is 11.55 (the minimum payment of 50 is reduced to match the debt) and the debt is
paid off.
- The total amount repaid on the debt is 116.
When calculating percentages the amount is rounded up to 2 decimal places. E.g. 10.201 and 10.
would both be rounded up to 10.21.
1(a) [ 26 marks ]
Write a program that reads in the interest percentage followed by the repayment
percentage. Percentages will be integers between 0 and 100 (inclusive).
You should output the total amount repaid.
You will always be given input that allows the debt to be paid off.
Sample run 1
10 50
116.
1(b) [ 2 marks ]
Given an interest percentage of 43% and a repayment percentage of 46%, how many payments will be
made to pay off the debt?
1(c) [ 3 marks ]
Which interest and repayment percentages (integers between 0 and 100) lead to the largest amount repaid
on a debt that is paid off?
Question 3: Serial Numbers
A serial number can be transformed into another, by swapping two adjacent digits, so long as one of
those two digits is adjacent to a digit whose value lies between them. Two serial numbers will be called
equivalent if there is a sequence of transformations which changes one into the other, and the distance
between them is the minimum number of such transformations required.
For example, the following shows all the serial numbers that are equivalent to 146235 , the lines showing
all the valid transformations:
146235
142635
461235 416235 412635 142365 124365 124635
412365
The distance from 461235 to 124635 is 6, and from 412635 to 142635 is 1.
3(a) [ 24 marks ]
Write a program that determines the largest distance between a serial number and
any equivalent number.
Your program should input a single integer d ( 1 ≤ d ≤ 9) indicating the number of
digits in the serial number, followed by a d digit serial number which will consist of
the numbers 1,..., d without repetition.
You should output a single integer giving the largest distance.
Sample run
6
3(b) [ 4 marks ]
What is the largest distance between any two serial numbers equivalent to 326451? How about
3(c) [ 6 marks ]
What is the size of the largest set of serial numbers, none of which are equivalent, each consisting of the
digits 1,...,5 without repetition? What is the size if the serial numbers consist of the digits 1,...,9 without
repetition?
Total Marks: 100 End of BIO 2018 Round One paper
