Math Patterns

Interview math is a small toolbox applied to disguised problems.

Think number theory when you see:

• Divisibility, remainders, “mod 10^9+7”
• Counting pairs/triplets with huge n → formula or precompute
• Powers that overflow → fast power
• “How many ways” → combinatorics

Quick Recognition Cheat Sheet

If you see…	Think…
Divisor / multiple / coprime	GCD (Euclid)
Primes up to n / prime checks	Sieve of Eratosthenes
Answer mod 10^9+7	Modular arithmetic
Huge exponent / repeated multiply	Fast power
”Number of ways to choose”	Combinatorics (nCr)
Points, lines, turns	Cross product

Pattern Table

Pattern	Typical Questions	Trigger
GCD / LCM	Water jug, fraction simplify	Divisibility language
Prime sieve	Count primes ≤ n	Many primality queries
Modular arithmetic	Big results mod p	Overflow risk
Fast power	pow(x, n), matrix power	Exponent too big to loop
Combinatorics	Unique paths, count sequences	”How many ways”

Mental Trigger

Overflow or huge loop? → math trick exists. Find it before coding brute force.

Decision Guide

Divisibility question
        ↓
   GCD via Euclid

Many primality questions
        ↓
   Sieve once, answer O(1)

Result too big / mod required
        ↓
   Modular rules + fast power + inverse

"How many ways"
        ↓
   nCr via Pascal or factorials