Loops and Conditions

A loop repeats steps; a condition (if–otherwise) chooses which step to do. Tracing a loop means tracking the values round by round.

Key ideas

A loop repeats a set of steps, so we do not have to write them again and again.
“Repeat k times” runs exactly k times; a while loop runs as long as its condition is true.
A variable is a name that stores a value, like x or score; “x = x + 2” makes x two more.
In a nested loop, the inner loop runs fully on every round of the outer loop.
An if–otherwise rule checks a condition each round and does only one of the two steps.
A robot drawing a regular shape turns a total of 360°, so each turn is 360° ÷ the number of sides.

Remember

Count from a to b in steps of s	(last number said − a) ÷ s + 1
x = a, repeat k times: x = x + d	x = a + k × d
x = a, repeat k times: x = x × 2	x = a × 2ᵏ
Repeat a times (repeat b times: clap)	a × b claps
Turn for a regular shape with n sides	360° ÷ n (square: 90°, hexagon: 60°)
While the box has less than ₹T, add ₹d	stop at the first total of ₹T or more

Watch out

Missing the first or the last number when counting the rounds of a loop.
Adding the inner and outer counts instead of multiplying them.
Stopping a while loop one round early: check the condition again after every round.

Worked example

(a) Start with n = 18.
While n is 84 or less: say n, then add 4 to n.
How many numbers are said?
(b) Isha's box has ₹30.
While the box has less than ₹745: add ₹50 and count one day.
How many days are counted?

Working: (a) 18, 22, …, 82: (82 − 18) ÷ 4 + 1 = 17; (b) ₹30 + 15 × ₹50 = ₹780, which is the first total of ₹745 or more

Answer: (a) 17; (b) 15