Packet puzzles: order the pieces

A message in smaller pieces

A message can travel in smaller pieces instead of one giant block. Our paper model labels each piece with a message name and a position. Real network protocols are more detailed and do not all make the same promises. Today we are studying a simple ordering problem.

Read both parts of the label

Message M needs three pieces. M one carries the word meet, M two carries at the, and M three carries library. The label and the words have different jobs. One helps organize the pieces; the other carries the message we want to reconstruct.

Arrival is not the answer

Our pieces arrive in the order three, one, two. Reading immediately in arrival order would scramble the message. Instead, use each position label. The last piece to arrive need not be the last piece in the sentence. Our desk is an organizer, not a race announcer.

Reconstruct the whole message

Place M one first, M two second and M three third. The reconstructed message is meet at the library. We know it is complete in this model because all three required positions are present for message M. Counting cards alone would not give us the same assurance.

Pause: inspect a new delivery

Here is a new message K that needs positions one, two and three. The received cards are K one, K three and another K three. Pause and identify the missing position. Then explain why having three cards does not prove that all three parts of the message arrived.

Check the missing piece

Position two is missing. Two copies of position three do not supply position two. In a system designed to request missing information, that gap can be a reason to request the missing part. We should not invent its contents or borrow a piece from a different message.

Three cards, two positions

Fun fact: three received cards can cover only two different positions. Our example has one, three and three. It is another reason to name what you count. Cards received and distinct message positions are different quantities, even when their numbers sometimes happen to match.

Keep the model honest

Continue to the worksheet below. Reconstruct the original message, inspect a duplicate and reject a piece labeled for another message. Keep the exercise on paper. It does not require sending traffic, collecting real addresses or scanning networks. The goal is careful reasoning about labeled information.