Representative Combinatorics problems
Calculate the number of unique paths for a robot to move on an m x n grid with only right and down movements.
Open problem page#458 Poor PigsFind the minimum number of pigs required to determine the poisonous bucket within a set time using state transition dynamic programming.
Open problem page#920 Number of Music PlaylistsSolve the Number of Music Playlists problem with dynamic programming, focusing on state transitions and combinatorics to calculate possible playlists.
Open problem page#1201 Ugly Number IIIFind the nth positive integer divisible by a, b, or c using binary search over the answer space efficiently and accurately.
Open problem page#1359 Count All Valid Pickup and Delivery OptionsCount all valid pickup and delivery sequences for n orders where deliveries occur after pickups using dynamic programming.
Open problem page#1467 Probability of a Two Boxes Having The Same Number of Distinct BallsCompute the probability that two boxes contain the same number of distinct balls using careful combinatorial and DP methods.
Open problem page#1569 Number of Ways to Reorder Array to Get Same BSTDetermine the number of ways to reorder an array to get the same binary search tree (BST) from its insertion order.
Open problem page#1621 Number of Sets of K Non-Overlapping Line SegmentsCount all valid arrangements of k non-overlapping line segments on n points using state transition dynamic programming.
Open problem page#1641 Count Sorted Vowel StringsCalculate the number of length-n strings with vowels only that are sorted lexicographically using state transitions.
Open problem pageCombinatorics interview questions usually collapse into a small set of repeatable moves. This page groups those GhostInterview problem pages together so you can stay inside one pattern family, compare representative questions, and practice explanations that transfer across multiple prompts. If you are trying to sharpen one interview weakness instead of browsing the entire library, start here.
Why Combinatorics Matters In Coding Interviews
Interviewers rarely care about the label alone. They care about whether you can recognize when the Combinatorics pattern applies, explain why it applies, and avoid the failure modes that usually show up under time pressure. That is why this page focuses on the family of problems rather than a single isolated example.
Pattern families that show up here
- State transition dynamic programming
- Array plus Math
- Array scanning plus hash lookup
Use this page to narrow the session
Start from this topic hub, choose one or two representative problems, and then open the detailed problem pages only after you know which version of the pattern you want to reinforce.
How To Practice This Topic
The best workflow is to keep the prep block narrow. Pick one easy or medium problem to confirm the base pattern, then one medium or hard problem to test whether the explanation still holds when the constraints tighten. Once the logic is stable, move into GhostInterview to rehearse the live explanation flow.
Focus on transfer, not title count
Solving more Combinatorics titles is less useful than understanding how the same move changes across examples. Try to describe what stays the same and what changes from one problem to the next.
Use the problem page when you want the exact breakdown
This topic hub is the discovery layer. The single-problem pages are where you get the answer-first summary, examples, constraints, approach, complexity, pitfalls, and solver CTA.
How GhostInterview Fits
GhostInterview works best after you know which pattern family you are inside. Use this page to choose the right Combinatorics problem, then use the solver to get the answer path, complexity framing, and follow-up support without switching into a generic study flow.
FAQ
What does the Combinatorics topic usually test in interviews?
Combinatorics questions usually test whether you can spot the underlying pattern quickly, explain the trade-offs, and move from intuition to implementation without losing clarity.
How should I use this Combinatorics topic page?
Use it as a pattern hub. Start with the representative problems on this page, compare the common approach, and then open the exact problem page when you want the full breakdown.
How many GhostInterview problem pages are in the Combinatorics group?
This topic page currently groups 49 indexed GhostInterview problem pages under the Combinatorics family.
Should I practice this topic before harder patterns?
That depends on your current gaps. If Combinatorics is already a weak spot in interviews, it is usually better to stabilize it first before moving into more advanced or less frequent patterns.
Where does GhostInterview fit once I pick a Combinatorics problem?
The topic page narrows the pattern family. The problem page gives the exact breakdown. GhostInterview is the solver layer when you need direct help with execution, complexity, and follow-up handling.
Stay close to the same reasoning family
Need direct help once you choose a Combinatorics problem?
Use GhostInterview as the solver layer after you select the exact prompt. Capture the question, get the answer path and complexity framing, and keep the workflow inside the same topic family.