# B Spy Extravaganza-Probability/Logic riddle

1. Aug 13, 2016

### Andreas C

The inspiration for this puzzle can be found here: http://mindyourdecisions.com/blog/2016/07/31/spies-sharing-secrets-sunday-puzzle/ . However, as is obvious from the unnecessarily convoluted character of the following two problems, the rest is original.

Part 1:
James Bond, Ethan Hunt, Sherlock Holmes, Hercule Poirot and Jason Bourne are all in a secret mission to gather certain secrets. At day 1, everyone has gathered one secret each. However, one spy doesn't know any of the secrets the other spies have gathered, and the secrets have to be shared through messages. Every spy can send only 1 message directed to 1 other spy at exactly 11:59PM of each day. All the spies send the messages at once. The messages are one way, meaning that the person who sends the message can not receive any information regarding the person that he sent it to (although he can chose a specific person to send the message to).

The contents of the messages are:
1) The name of the spy who sent the message.
2) The date when the message was sent.
3) The secret that the spy who sent the message has discovered.
4) All the previous messages that a spy who sent the message has received.

The spies have no other way to communicate with each other, so they can't know how many messages another spy may have received, unless they get a message from that spy. At noon of day 4 every spy who does not know all of the secrets will blow his cover and will be killed. Study the possibilities and find the best strategy for the spies in the following scenarios:

On day 1, the following spies send messages to these people:
Scenario A:
Bond->Hunt
Hunt-> Holmes
Holmes-> Poirot
Poirot-> Bourne
Bourne-> Bond

Scenario B:
Bond-> Poirot
Hunt-> Poirot
Holmes-> Hunt
Poirot-> Hunt
Bourne-> Bond

Scenario C:
Bond-> Hunt
Hunt-> Bond
Holmes-> Poirot
Poirot-> Holmes
Bourne-> Poirot

OPTIONAL: What happens if there are 10 spies (executed at noon of day 9), with a scenario similar to scenario A (all of the spies receive one message)?

Part 2:
Similar rules, but now spies will start being executed from the noon of day 2. Each secret that they know will help them survive another day, meaning that if a spy has 1 secret extra to what he already knows, he will be killed at the noon of day 3. If he has 2 extra ones, at day 4, etc. Every spy who lives up to day 6 will escape.

If a message is sent to a dead spy, the message is returned, so the spy who sent it learns that the other spy is dead. That information will be contained in the next message the spy will send. However, the spy will only know if the message has been returned just before 11:59PM of the next day, so one spy can't send another message in the same night if he has already sent one that has been returned.

What is the maximum number of spies that will escape and what is the possibility that that will happen in each scenario? What should the spies do to maximize that?

OPTIONAL: Similar rules, 10 spies, 11 days to escape.

2. Aug 13, 2016

### Andreas C

By the way, Part 2 is much easier than Part 1, so you may want to try that one first. Oh, and the prefix shouldn't have been beginner. Maybe there's a way to change it?