Mastering Loop Logic: 30 Loop Problems to Practice Solving

1. How many times does the following loop execute?

i = 0
found = False
while i < 100 and found != True :
   i = i + 1
   print(i, end = " ")
   j = i * i
   if i * i * i % j == j :
      found = True

An infinite number of time

1. Initially, i is set to 0, and found is set to False.
2. The loop condition i < 100 and found != True checks two conditions: whether i is less than 100 and whether found is not equal to True.
3. Inside the loop, i is incremented by 1 in each iteration (i = i + 1).
4. Then, j is calculated as the square of i.
5. The if condition if i * i * i % j == j is checked. This condition will always be true because i * i * i is always divisible by j (which is i * i).
6. As a result, found is set to True.
7. However, since the loop condition checks both i < 100 and found != True, and i is incremented in each iteration, i will eventually reach a value greater than or equal to 100, but the loop will continue to execute because the condition found != True remains true due to found being set to True only after the if condition inside the loop.