Introductory Exercises

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.

k^th digit

Extract the k^th 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.