Qm
BrainteasersJane StreetCitadel

The dinner party handshakes

logichandshakesgraphsclassic

Five married couples, including the host and the host's partner, meet at a party. Some people shake hands. Nobody shakes hands with their own partner, and no pair shakes hands more than once. Afterwards the host asks each of the other nine people how many hands they shook, and gets nine different answers.

How many hands did the host's partner shake?

Show a hint

Each person can shake at most 8 hands (10 people, minus themselves and their partner). Nine different answers from 0 to 8 means every number from 0 to 8 appears once. Pair up the person who shook 8 with the person who shook 0.

Your answer

Solving needs a free account

Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.

Create a free accountSign in

Discussion

Sign in to join the discussion · reading is open to everyone

💡 Discussion rules

  1. No full solutions here. Hints and approaches only.
  2. Complexity, edge cases and intuition are the point.
  3. Interview experiences are welcome. Respect your NDAs.

Loading discussion…

Learn the concepts

The theory behind this question.

Cheryl's Birthday and Iterated KnowledgeGraph Traversal, BFS and DFSGraph Theory BasicsLogic and QuantifiersOne Question, Two Guards, One Door

Related questions

Ali and the eight loavesThe blind man and the four pillsCan 21 people each shake exactly three hands?Knights, knaves, and the fork in the roadThe lion, the unicorn and the day of the week
All questions →