#combinatorics

11 combinatorics interview questions, asked at Amazon, Google, Snowflake and 3 more companies. Last asked Oct 2026.

Count ordered routes that visit one shop of each of four typesCodingYou need four things from four kinds of shop: a bookshop, a school-supply shop, a sports store and a stationery store. The town has many shops of each kind, joined by roads…
Last asked Oct 2026
Count grid paths through ordered checkpointsCodingAn n x m grid. A path starts at the bottom-left cell and ends at the bottom-right cell. Each move goes one column to the right and either one row up, the same row, or one row…
Last asked Sep 2026
N-th number whose digits are all 3, 5 or 6CodingA good number is a positive integer whose decimal digits are all 3, 5 or 6: 3, 5, 6, 33, 35, 36, 53, ... Given n, return the n-th good number. Notice the link to counting in base…
Last asked Sep 2026
Find every set in a hand of Set cardsCodingEach card in the game Set has four attributes (color, shape, number, shading), and each attribute takes one of three values, so a card is four numbers from 0 to 2. Three cards…
Last asked Jul 2026
Most common website visit patternCodingGiven which user visited which website and when, find the sequence of three websites that the most users visited in that order.
Last asked May 2026
Uniformly random spanning tree over node groupsCodingYou are given groups, a list of K disjoint, non-empty lists of integer node IDs. Nodes inside a group are already connected to each other; different groups are not connected. You…
Last asked May 2026
N-th license plate in sorted orderCodingLicense plates follow a fixed format, for example three letters A-Z then three digits 0-9 (AAA000). Sorted in dictionary order, what is the n-th plate? Compute it directly by…
Last asked Jun 2025
Fill a weekly work schedule to an exact hour totalCodingA week's work plan is written as a 7-character string pattern, one character per day. A digit (0-9) is a day whose hours are already set. A ? is a day that is still open…
Pascal triangle digit encryptionCodingDigits are encrypted by folding them down an upside-down Pascal's triangle. You get a list of n digits (each 0-9). In one round, replace the list with the sums of each pair of…
Count distinct passwords from one substring reversalCodingA security team scores a password by its variability. Variability is the number of distinct strings you can get by reversing exactly one contiguous substring of the password…
Count colorings of a row of houses with fixed end colorsCodingA contractor is repainting a row of n houses, numbered 0 to n - 1. There are k paint colors, numbered 0 to k - 1. The new paint job must follow two rules: - Two neighboring houses…