Unit #1 and Unit #2
Problem #1: A perfect
number is a positive integer (more than 0) whose factors except the number add
up to the number. For example – The factors of 6 except itself are 1, 2 and
3.1+2+3 =6. Hence, 6 is a perfect
number. Write a program which takes an integer input and prints if the input is
a, “perfect number” or, “not a perfect number”.
Example:
Run #1:
Input number
28
Program Output:
28 is a perfect number
Run #2:
Input number
50
Program Output:
50 is not a perfect number
Problem #2: Write
a program to print all the terms in the Fibonacci sequence that are less than 100.
Program
Output:
0 1 1 2
3 5 8 13 21 34 55 89
Unit #3
Problem #3:
A happy number is defined by the following process.
Starting with any positive integer (>0), replace the number by the sum of
the squares of its digits, and repeat the process until the number equals
1(happy) or 4(unhappy). Write
a program which taken a non-zero, positive integer input, N and outputs if it’s
happy or unhappy.
Example Input/output:
·
7 is a happy number since 7 -> 49 -> 97 ->
130 -> 10 -> 1.
·
4 is an unhappy number since 4 -> 16 -> 37
-> 58 -> 89 -> 145 -> 42 -> 20 -> 4.
·
45 is an unhappy number since 45 ->
41->17->50->25->29->85->89->145->42->20->4
Problem #4:
A
humble number is a positive integer (> 0) whose only prime factors are 2 or 3 or
5. Your program will take a positive integer input (> 0) and output
if it’s humble or not.
Example Input/output:
·
Input:
35; Output: Not a Humble number;
·
Input:
15; Output: Humble number;
·
Input:
100; Output: Humble number;
Problem #5:
Almost
prime numbers are the non-prime numbers, which are divisible by only a single
prime number. In this problem, your job is to write a program, which finds out
the number of almost prime numbers within a certain range. The input to you program will be two integers
(x and y), which specify the range, [x, y]. The output will be a count (n) of
the non-prime numbers in that range. You can test your program with the
following:
Interval [x,y] Count(n)
[1,
10] 3
[1 , 20] 4
Problem #6:
In 1994, Mexico’s population was 58 million and growing at the annual rate of
7%. The United States’ population in the same year was 260 million and growing
at the annual rate of 2%. If these two countries were to maintain the current
rates of growth, in how many years will Mexico’s population exceed that of the
United States. (Answer: 32 years)
NOTE: Use a double variable type to store the real
numbers that you will encounter in this problem.
Program
Output:
Year#1
Mexico = 62.060 USA = 265.200
Year#2
Mexico = 66.404 USA = 270.504
Year#3
Mexico = 71.052 USA = 275.914
Year#4
Mexico = 76.026 USA = 281.432
Year#5
Mexico = 81.348 USA = 287.061
Year#6
Mexico = 87.042 USA = 292.802
Year#7
Mexico = 93.135 USA = 298.658
Year#8
Mexico = 99.655 USA = 304.631
Year#9
Mexico = 106.631 USA = 310.724
Year#10
Mexico = 114.095 USA = 316.939
Year#11
Mexico = 122.081 USA = 323.277
Year#12
Mexico = 130.627 USA = 329.743
Year#13
Mexico = 139.771 USA = 336.338
Year#14
Mexico = 149.555 USA = 343.064
Year#15
Mexico = 160.024 USA = 349.926
Year#16
Mexico = 171.225 USA = 356.924
Year#17
Mexico = 183.211 USA = 364.063
Year#18
Mexico = 196.036 USA = 371.344
Year#19
Mexico = 209.759 USA = 378.771
Year#20
Mexico = 224.442 USA = 386.346
Year#21
Mexico = 240.153 USA = 394.073
Year#22
Mexico = 256.963 USA = 401.955
Year#23
Mexico = 274.951 USA = 409.994
Year#24
Mexico = 294.197 USA = 418.194
Year#25
Mexico = 314.791 USA = 426.558
Year#26
Mexico = 336.826 USA = 435.089
Year#27
Mexico = 360.404 USA = 443.790
Year#28
Mexico = 385.633 USA = 452.666
Year#29
Mexico = 412.627 USA = 461.720
Year#30
Mexico = 441.511 USA = 470.954
Year#31
Mexico = 472.417 USA = 480.373
Year#32
Mexico = 505.486 USA = 489.981
Time in Years will be 32
Problem #7:
NOTE: Use the double variable type for this
problem.
Calculate the value of π (up to four decimal places) from the
following series:
π = 4 – 4/3 + 4/5 - 4/7 +
4/9 - 4/11 +…..n terms
The
program will take a positive integer, n (>0) as the input, which represents
the number of terms in the series.
Example input/output:
·
If n =10, π=3.0418
·
If n = 100, π=3.1316
·
If n = 1000, π=3.1406