How many two-digit numbers have the unit digit of their square equal to 8?

Problem restatement
Count two-digit integers n such that the last digit of n² is 8.

Concept/Approach
Squares modulo 10 only take certain last digits: for units digit d ∈ {0,…,9}, d² ends with {0,1,4,9,6,5,6,9,4,1} respectively.

Step-by-step reasoning
No square ends with 8 for any digit 0–9.

Final Answer
0