Next Greater Numerically Balanced Number

Next Greater Numerically Balanced Number

What is this problem about?

The Next Greater Numerically Balanced Number problem asks for the smallest integer greater than n such that every digit in the number appears exactly as many times as its own value (e.g., 1 appears once, 2 appears twice, 3 appears three times). This Next Greater Numerically Balanced Number coding problem uses enumeration from n+1 upward with a digit-count validation check.

Why is this asked in interviews?

Sprinklr, Microsoft, Meta, and Bloomberg ask this to test the ability to implement a custom validation function and apply it through enumeration. The math, hash table, counting, enumeration, and backtracking interview pattern is applied, and the problem rewards candidates who recognize the bounded search space (balanced numbers are sparse and don't grow too large).

Algorithmic pattern used

Enumeration with digit-count validation. Starting from n+1, check each number: count the frequency of each digit and verify that each digit d appears exactly d times. Return the first valid number found. The valid numbers are sparse enough that enumeration terminates quickly in practice.

Example explanation

n = 1. Check 2: count {2:1}, 2 should appear 2 times → invalid. Check... 1211: {1:2,2:1} → 1 appears 2 times but needs 1, invalid. 1333: {1:1,3:3} → 1 appears 1 time ✓, 3 appears 3 times ✓. Valid! → 1333.

n=7: Next balanced number with digit property... 1333 (first balanced > 7 if not already past it).

Common mistakes candidates make

• Not checking that every digit in the number satisfies the condition (only checking some digits).
• Forgetting that digit 0 appearing in the number is automatically invalid (0 must appear 0 times, i.e., never).
• Infinite loop if termination condition is missed (valid numbers always exist).
• Off-by-one in the starting point (must start from n+1, not n).

Interview preparation tip

Enumeration problems with custom validity conditions follow the template: (1) write the validation function cleanly, (2) iterate from the next candidate, (3) return the first valid result. The key is making the validation function O(digits) = O(1) for bounded integers. Practice writing clean digit-counting validators: use array count[10] for digit frequencies and verify against digit values. This pattern appears in "special number" problems across multiple companies.