Introductory Exercises
Contents
- 1 Introductory Exercises
- 1.1 Problems with numbers (no sequences as input)
- 1.1.1 First Degree Equation i
- 1.1.2 Second Degree Equation i
- 1.1.3 Divisibility Test i
- 1.1.4 Leap Year Test i
- 1.1.5 kth digit
- 1.1.6 Triangle Edges i
- 1.1.7 Swap Variables i
- 1.1.8 Swap Variables Restricted i h
- 1.1.9 Divisors
- 1.1.10 Primality
- 1.1.11 Reverse Digits
- 1.1.12 Multiple Count i h
- 1.1.13 Leap Year Count i h
- 1.1.14 Palindrome h
- 1.1.15 Sort numbers i
- 1.1.16 Sort more numbers i h
- 1.1.17 GCD and LCM
- 1.1.18 Prime Factors
- 1.1.19 Numbers with two digits
- 1.1.20 Decimal Fraction h
- 1.1.21 Number Guessing
- 1.1 Problems with numbers (no sequences as input)
Introductory Exercises
This is a small list of exercises for beginners. Some of them require minimal math knowledge. I will try and make references to that knowledge, when possible.
Problems with numbers (no sequences as input)
First Degree Equation i
Solve the first degree equation with one variable: ax + b = 0, given a and b as input.
Second Degree Equation i
Solve the second degree equation with one variable: ax2 + bx + c = 0, given a, b and c as input.
Divisibility Test i
Find out if n is divisible by k.
Leap Year Test i
Find out if year y is a leap year.
kth digit
Extract the kth digit of a number, counting digits from right to left
Triangle Edges i
Can three input numbers be the lengths of the three edges of a triangle?
Swap Variables i
Given variables a and b exchange their values so that in the end a will contain the old value of b and b will contain the old value of a.
Swap Variables Restricted i h
Given variables a and b exchange their values so that in the end a will contain the old value of b and b will contain the old value of a, without using any other variables.
Divisors
Display all of number n's divisors.
Primality
Is number n a prime number?
Reverse Digits
Display in reverse order the digits of a number n
Multiple Count i h
How many integers divisible by n lie in interval [a, b]?
Leap Year Count i h
How many years between y1 and y2 are leap years?
Palindrome h
Is number n a [palindrome]? A palindrome is a symmetrical number, like 15351 or 12233221.
Sort numbers i
Display three input integers in ascending order.
Sort more numbers i h
Display five input integers in ascending order. Make the flow chart fit on one letter page.
GCD and LCM
Find the [greates common divisor] and the [lowest common multiple] of two numbers. Use [Euclid's algorithm]. Example: GCD of 24 and 32 is 8.
Prime Factors
Display the [prime factor decomposition] of input number n. Example: 1176 = 23 x 31 x 72
Numbers with two digits
Is number n formed with exactly 2 digits repeated any number of times? 23223 and 900990 are such numbers, while 593 and 44002 are not.
Decimal Fraction h
Display fraction m/n in decimal format, with the period between brackets. Example: 13/30 = 0.4(3)
Number Guessing
Guess a number between 1 and 1024 by asking questions of the form "is the number greater or equal to x".
Legend:
- i means that the problem can be solved without loops, using only if-then-else structures.
- h means hard. The problem is difficult.
