Consensus and Why Agreement Is Hard · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

How five machines say yes together

Computing · Networks & Security · ages 20-21
Name ______________________   Date ____________

  1. Two majorities of five nodes overlap in at least how many nodes? Type the number.

    Answer: ______________

  2. Five nodes vote. How many make a majority?

    • Two
    • Three
    • Four

  3. Two majorities of five nodes can decide conflicting values with no overlap.

    Circle one:   True   False

  4. 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

  5. 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

  6. What job does the leader do in practice?

    • It stores every value forever
    • It gathers votes and announces the single decision
    • It speeds up all clocks

  7. A team uses groups of 2 from 5 as quorums to go faster. Two groups pick different values. What broke?

    • Groups of 2 need not overlap, so conflicting decisions became possible
    • Groups of 2 are slower than groups of 3
    • Five nodes are too few for any quorum

  8. A protocol designer promises safety plus guaranteed progress even when delays have no bound. What does theory say?

    • It is achievable with enough nodes
    • It is ruled out; unbounded delay forbids both at once
    • It needs a faster leader only
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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. 1 · Two groups of 3 from 5 must share at least one member.
  2. Three · Three is the smallest group beating every smaller one.
  3. False · Overlap is forced, and the shared node votes only once.
  4. Step down, since the newer term wins · One leader per term keeps decisions single, so the elder yields.
  5. The shared node votes only once, blocking the rival decision · One member belongs to both groups, so it cannot back both sides.
  6. It speeds up all clocks · Coordination through one announcer is what makes agreement practical.
  7. Groups of 2 need not overlap, so conflicting decisions became possible · Without forced overlap nothing stops two groups from deciding apart.
  8. It is ruled out; unbounded delay forbids both at once · Waiting risks stalling while deciding risks splitting, with no way to have both.
Worksheet · LightMySky