Representative Number Theory problems
Count all prime numbers less than a given integer n using efficient array and math-based enumeration techniques.
Open problem page#258 Add DigitsAdd Digits involves repeatedly summing digits of a number until a single digit is obtained.
Open problem page#858 Mirror ReflectionGiven a square room with mirrors, find which receptor a laser ray will hit first based on two integers, p and q.
Open problem page#866 Prime PalindromeThe Prime Palindrome problem asks for the smallest prime palindrome greater than or equal to a given integer.
Open problem page#914 X of a Kind in a Deck of CardsSolve the problem of determining if a deck can be partitioned into groups with equal occurrences of card values.
Open problem page#952 Largest Component Size by Common FactorFind the largest connected component in an array where edges exist between numbers sharing a common factor greater than one.
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#1250 Check If It Is a Good ArrayDetermine if a given array of positive integers can generate 1 using integer multiples of any subset, leveraging number theory.
Open problem page#1447 Simplified FractionsGenerate simplified fractions between 0 and 1 with denominators up to a given integer n.
Open problem pageNumber Theory 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 Number Theory Matters In Coding Interviews
Interviewers rarely care about the label alone. They care about whether you can recognize when the Number Theory 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
- Array plus Math
- Array scanning plus hash lookup
- State transition dynamic programming
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 Number Theory 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 Number Theory 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 Number Theory topic usually test in interviews?
Number Theory 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 Number Theory 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 Number Theory group?
This topic page currently groups 73 indexed GhostInterview problem pages under the Number Theory family.
Should I practice this topic before harder patterns?
That depends on your current gaps. If Number Theory 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 Number Theory 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 Number Theory 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.