Consider the following algorithm: Step 1: Start with a list of the positive integers from 2 to 100, inclusive (meaning you include 2 and 100 in your list).

Step 2: For each $n$ from 2 to 50, inclusive, do the following: Remove all multiples of $n$ greater than $n$ from the list.

Step 3: Output all of the numbers remaining in the list.

What is the tenth number in the list that gets output?

The tenth number in the list that gets output is 29

Explanation:

To get this done, the algorithm has to be implemented using a programming language;

The algorithm is translated to Python Programming Language as follows (Comment explains difficult lines);

#Declare an empty list

mylist = []

#Input n = 2 to 100 to list

for n in range(2,101):

    mylist.append(n)

#Iterate from 2 to 50

for n in range(2,51):

#Initialize first multiple of n

    k = 0

#Iterate multiples of n

    for j in range(n,51,n):

         k = k + 1

#Check if item exist

         if j in mylist:

#Print multiples of n greater than n

              if not k == 1:

                   mylist.remove(j)

#Print All List

print("List: ",mylist)

#Print 10th element of the list

print("10th Element: ",mylist[9])

After running the program, the output is as follows:

List:  [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]

10th Element:  29

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