Count three-digit numbers with distinct digits

Q: Count three-digit numbers with distinct digits

This question evaluates a candidate's understanding of digit manipulation, basic combinatorics, and implementation of value-range constraints in coding problems. As a Coding & Algorithms problem it is commonly asked because it reveals attention to edge cases and correctness when counting under bounds, testing practical implementation skills rather than purely theoretical reasoning.

Q: How do I approach Coding & Algorithms interview questions?

Coding & Algorithms questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master coding & algorithms interviews.

Question

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Problem

Given two integers left and right such that 100 ≤ left ≤ right ≤ 999, count how many three-digit integers x in the inclusive range [left, right] have all three digits distinct (i.e., no two digits are the same).

A three-digit number x has digits a (hundreds), b (tens), c (ones). It is valid if a, b, and c are all different: a != b, a != c, and b != c.

Input

Two integers: left , right .

Output

A single integer: the count of valid numbers in [left, right] .

Constraints

100 ≤ left ≤ right ≤ 999
The intended solution should run in time no worse than O(right^2) (a straightforward scan from left to right is acceptable).

Example

Input: left = 120 , right = 130
Output: 8
Explanation: Valid numbers are 120, 123, 124, 125, 126, 127, 128, 129 (numbers like 121 or 122 are invalid due to repeated digits).