Step 1: Recall what controls HCN addition.
HCN adds to the carbonyl carbon as a nucleophile. The reaction is easier when the carbonyl carbon is more positive and more open to attack.
Step 2: Note the two opposing effects.
More alkyl groups push electrons onto the carbonyl carbon (lowering its positive charge) and also crowd around it (steric hindrance). Both effects lower reactivity.
Step 3: Compare the three compounds.
Acetaldehyde \((CH_3CHO)\) has only one small alkyl group, so it is the most reactive. Acetone \(((CH_3)_2CO)\) has two methyl groups, so it is less reactive. Di-tert-butyl ketone has two very bulky tert-butyl groups, so it is the least reactive.
Step 4: Place them in order.
Least reactive is di-tert-butyl ketone, then acetone, then the most reactive acetaldehyde.
Step 5: Write the increasing order.
Increasing reactivity means least to most.
Answer: Di-tert-butyl ketone < Acetone < Acetaldehyde (increasing order of reactivity towards HCN).