Question

Q 7: What is the number of `Hello's printed by the pseudo code below? (for i from lo to hi
exhaust i between lo and hi inclusive, and is a empty loop when lo is greater than hi)
(b) for i from 1 to 10
for j from i to 10
for k from i to j
print `Hello'

Answer 1

Try some samples to see:
i = 1, j = 1: k from 1 to 1 --> 1 Hello
i = 1, j = 2: k from 1 to 2 --> 2 Hellos
i = 1, j = 3: k from 1 to 3 --> 3 Hellos
.
.
.
i = 1, j = 10: k from 1 to 10 --> 10 Hellos
So for i = 1, sum the numbers from 1 to 10 (triangular formula): (10)(10 + 1)/2 = 55 Hellos

Now try for i = 2:
i = 2, j = 1: k from 2 to 1 --> lo greater than hi, so no Hellos
i = 2, j = 2: k from 2 to 2 --> 1 Hello
i = 2, j = 3: k from 2 to 3 --> 2 Hellos
.
.
.
i = 2, j = 10: k from 2 to 10 --> 9 Hellos
So for i = 2, sum the numbers from 1 to 9 (triangular formula again): (9)(9 + 1)/2 = 45 Hellos

Now try for i = 3:
(Can you see the pattern emerging, by looking at the results of i = 1 and i = 2? This time, you should end up summing the numbers 1 to 8 for the number of Hellos.)

Etc.
At the end, sum up your sums to get the total number of Hellos.