My first instinct was to check pairs, which was completely wrong.
Clarify that the problem reduces to finding the digit (0-9) that appears in the most numbers, since any valid subset must share at least one common digit. Then propose an efficient O(n) solution using a frequency array of size 10, and discuss edge cases like numbers with repeated digits and empty input.
Pro tip: Mention that you can solve it in one pass by updating a count array for each digit in each number, and that the maximum count directly gives the subset size. This shows you can optimize beyond brute force and handle large inputs gracefully.
Ask whether the subset must be contiguous, whether numbers can be used multiple times, and what to return if multiple digits tie. Confirm that the subset is defined by a single common digit shared by all numbers.
Realize that any valid subset corresponds to choosing a digit d that appears in every number of the subset. Therefore, the largest subset size is the maximum frequency of any digit across all numbers.
Use a frequency array of size 10. For each two-digit number, extract its tens and units digits, and increment the count for each unique digit in that number. Track the maximum count seen.
State that the algorithm runs in O(n) time and O(1) space. Discuss edge cases: empty list, numbers with repeated digits (e.g., 11), and ties where multiple digits yield the same maximum count.
Walk through a small example, such as [12, 23, 34, 45], to show the frequency counts and the resulting maximum subset size. Summarize the solution and its efficiency.
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