Homework 3 Loops (while/for/do while). Nested loops

3. Loops (while/for/do while). Nested loops.
3.01. Fizz buzz is a group word game for children to teach
them about division. Players take turns to count
incrementally, replacing any number divisible by three with
the word "fizz", and any number divisible by five with the
word "buzz". Numbers divisible by 15, which is both become
fizz buzz. For example, a typical round of fizz buzz would
start as follows:
1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13,
14, Fizz Buzz, 16, 17, Fizz, 19, Buzz, Fizz, 22, 23, Fizz,
Buzz, 26, Fizz, 28, 29, Fizz Buzz, 31, 32, Fizz, 34, Buzz,
Fizz, ...
Writing a program to output the first 100 FizzBuzz numbers.
3.02. Write a program which calculates the arithmetic mean of
the digits of a given integer long long number, formatted to
the second digit after the decimal point.
3.03. Write a function with signature int digitPos(long long
num, int k), which returns the k-th digit of the number num
or -1 if such position does not exist. It starts counting
from left to right and from 1. For example: digitPos(1234, 3)
returns 3.
3.04. Write a function with signature double sqrt_x(double x,
double eps), which calculates a square root of x with an
epsilon (eps) precision.
3.05. Write a program which asks the user for a long long
number and then prints:
- the same number in binary;
- the same number in oct;
- the same number in hex.
3.06. Write a program which asks the user for a number n and
then prints whether n is a prime number or not.
3.07 Write a program wchich asks the user for a number n and
then prints all prime numbers smaller than n.
3.08. Write a program which asks the user for a number n and
then prints all prime factors of n.
3.09. Write a program which checks whether a number can be
expressed as a sum of two prime numbers.
3.10. Wtire a program which asks the user for a number n and
then prints a square with numbers with as many rows as n.
Align all numbers in the square!
• For n=3, the output must be; • For n=4, the output must
be (note how all columns are aligned)
1 2 3 1 2 3 4
4 5 6 5 6 7 8
7 8 9 9 10 11 12
13 14 15 16

3.11. Wtire a program which asks the user for a number n and
then prints a triangle with numbers with as many rows as n.
This right-angled triangular array of natural numbers is
named after Robert Floyd. Align all numbers in the triangle!
• For n=4, the output must be; • For n=7, the output must
be (note how all columns are aligned)
1 1
2 3 2 3
4 5 6 4 5 6
7 8 9 10 7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
3.12. Consider the sequence: 1;2+3;4+5+6;7+8+9+10;... . In
other words, the n-th term of the sequence is the "sum of the
next n natural numbers" - Felice Russo. Write a program which
prints the first n terms of the sequence.
Example input Expected output
225 3.3.5.5
31668 2.2.3.7.13.29
3.13. Write a program which checks to which row and column in
the Floyd's triangle the number n belongs.
3.14. Wtire a program which asks the user for an odd number n
and then prints a Christmas tree as wide as n. Print and
error if n is not odd!
• For n=5, the output must be: • For n=7, the output
must be:
* *
*** ***
***** *****
* *******
*
3.15. Write a program which asks the user for an odd number n
and then prints a heart as wide as 2n+1. Print and error if n
is not odd!
• For n=3, the output must be: • For n=5, the output
must be:
* * * *
*** *** *** ***
***** ***** *****
*** *********
* *******
*****
***
*
3.16. Ask a friend to take a piece of paper and write down a
number from 1 to 1000, without showing it to you. Write a
program that guesses the written number only by asking
questions like “Is your number bigger than {arbitrary number
of your choice}?”, etc. The program should ask minimum number
of questions. If the question contains the correct answer,
then your friend needs to answer with “that's the number!”,
otherwise with “yes” or “no”. Assuming your friend is not
lying, how many questions will your program ask in the worst
case?
3.17. Write a function with signature double calc(double a,
double b, double eps, long end), which calculates
. The calculations end
when . If k becomes greater than n - the function
must return a code for error.
3.18. Write a program which calculates the sum
and find the Napier's constant. The
approximation continues until the absolute value of the last
collectible becomes less than (where x and are given real
numbers).

3.19. Find the smallest number expressible as the sum of two
cubes in two different ways and print the expressions. (Taxi
number) ([Hardy–Ramanujan number](https://en.wikipedia.org/
wiki/1729_(number)) )

3.20. Write a program that reads an integer number N and
prints how many trailing zeros are present at the end of the
number N! (N factorial). Make sure your program works for N
up to 50 000. Hint: you don’t need to calculate the actual
factorial to count the number of trailing zeroes.
xk = 1
5 (xk−1 +
xk−1
xk−2 ), k = 3,4,...; x1 = a 0,x2 = b
| xk − xk−1 | < ϵ
ex = 1 +
x
1!
+
x2
2!
+ . . .
ϵ ϵ
Example
input
Expected
output
Explanation
1 0 1!=1, no trailing zeros
5 1 5!=120, 1 trailing zero
20 4 20!=2432902008176640000, 4 trailing zeros