En anglais

How five machines say yes together

Computing · Networks & Security · ages 20-21

Name ______________________ Date ____________

Nine nodes decide by majority, so each majority has 5 nodes. At least how many nodes must two majorities share? Type the number.
Answer: ______________
Seven nodes vote. What is the smallest number of votes that makes a majority?
- Three
- Four
- Five
In a cluster of five nodes, two majorities can decide conflicting values with no overlap.
Circle one: True False
An old leader returns after the network heals and finds a newer term in charge. What should it do?
- Rule beside the new leader
- Step down, since the newer term wins
- Order a fresh vote at once
Within one round of voting, why does the overlap make two conflicting decisions impossible?
- The shared node votes only once, blocking the rival decision
- Majorities run on faster machines
- Five is an odd number
What job does the leader do in practice?
- It stores the only copy of every value for the cluster
- It gathers votes and announces the single decision
- It syncs every node's clock so timestamps decide the order
A team uses groups of 2 from 5 as quorums to go faster. Two groups pick different values. What broke?
- Two groups of 2 can be disjoint, so they decided apart
- Groups of 2 are slower than groups of 3, so votes arrived late
- Five nodes are too few for any quorum to work safely
A designer promises a deterministic protocol with safety plus guaranteed progress, even when delays have no bound and one node may crash. What does theory say?
- It is achievable once the cluster has enough nodes
- It works as long as the leader runs on fast hardware
- It is ruled out, since that model forbids both

Answer key

For grown-ups. Fold this page away before handing over the rest.

How five machines say yes together W1-mt_cF-JiM_xRz-s1

1 · Two groups of 5 drawn from 9 nodes share at least 5 + 5 - 9 = 1 node.
Four · A majority is more than half. Half of 7 is 3.5, so 4 votes is the smallest majority.
False · Overlap is forced, and the shared node votes only once.
Step down, since the newer term wins · Only one leader may rule per term, so the old leader steps down.
The shared node votes only once, blocking the rival decision · In one round, one member belongs to both groups and votes once, so it cannot back both sides.
It gathers votes and announces the single decision · Coordination through one announcer is what makes agreement practical.
Two groups of 2 can be disjoint, so they decided apart · Two pairs from five nodes can share no node, so nothing stops them deciding different values.
It is ruled out, since that model forbids both · With unbounded delay and a possible crash, waiting risks stalling and deciding risks splitting, so no deterministic protocol can guarantee both.