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The teacher of my nephew (15y) proposed the following puzzle to the students. I solved it, but I found it extremely difficult, in particular for teenagers. Perhaps there is a simpler solution than mine.

Additionally, I suspect that the puzzle is not original, but I was unable to find one with the same or equivalent formulation. Can anyone identify the source?

This is the problem:

Five thieves are about to strike. Each one will play a specific role: the hacker will disconnect the security system, the overlooker will check the environment, the driver will be ready for the escape in the car, the driller will break the safety box and the accessory after the fact should be ready to get rid of the booty. The five thieves are called Albert, Bob, Charley, Damian and Ernest.

Who hired them (the boss) wants them to meet, so that they can know each other, since some of them have never met before (but others have already coincided in other misdeeds).

The hacker and the overlooker do not attend to the meeting. The boss realizes that: Bob will never know the accessory after the fact, Charley knows the driver, Damian knows only one of the thieves, Ernest knows three of them, Albert knows only two of them, the hacker is the only one which knows only one other, and finally the overlooker knows other three.

Which character plays which role?

(Sorry if the translation is not very good, the original is in Spanish. Feel free to ask for clarifications or suggest improvements in the comments)

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  • $\begingroup$ This seems like a standard logic problem that I might have encountered in jr. high and high school. I certainly don't think 15 is too young to be able to solve this type of problem. $\endgroup$ – ell Jan 2 '17 at 22:30
  • $\begingroup$ All the solutions below assume that only the hacker and the overlooker missed the meeting. In fact you need to make this assumption to be able to solve the problem: if the driller also missed the meeting then a possible solution is A driver, B driller, C accessory, D hacker, E overlooker, with pairs who know each other being AC, AE, CE and DE. However, the text you provide does not say that. Does the original version? $\endgroup$ – Especially Lime Jan 3 '17 at 13:45
  • $\begingroup$ @EspeciallyLime No, the original version doesn't make clear that only two persons missed the meeting (although it is somewhat implied). Interesting point. $\endgroup$ – JLDiaz Jan 4 '17 at 13:25
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We start with some easy observations:

  • "Damian knows only one of the thieves" and "the hacker is the only one which knows only one other": This implies that Damian is the hacker

  • "The hacker and the overlooker do not attend to the meeting" implies that the accessory after the fact attends the meeting. "Bob will never know the accessory after the fact" implies that Bob does not attend to the meeting. Hence Bob is the overlooker.

  • This means that Albert, Charley, and Ernest are the three guys who attend the meeting.

Now we analyze the acquaintance structures. This is under the assumption that "knowing" is always mutual:

  • Albert, Charley, and Ernest each know at least the two other guys from the meeting.

  • "Albert knows only two of them" implies that Albert knows Charley and Ernest, but nobody else.

  • "the overlooker (Bob) knows other three" implies that Bob knows Charley, Damian, and Ernest (as Bob doesn't know Albert)

  • "Ernest knows three of them" implies that Ernest knows Albert and Charley (from the meeting) and Bob (as Bob knows Ernest)

  • "Damian knows only one of the thieves" implies that Damian knows Bob and nobody else.

  • This finally leaves that Charley knows Albert, Bob, and Ernest (but not Bob).

Now let us finally wrap things up:

  • "Bob will never know the accessory after the fact" and Bob knows everybody except Albert implies that Albert is the accessory after the fact

  • "Charley knows the driver" implies that Charley himself is not the driver, which means that Charley is the driller

  • This finally yields Ernest is the driver

To summarize the solution:

  • Albert is the accessory after the fact

  • Bob is the overlooker

  • Charley is the driller

  • Damian is the hacker

  • Ernest is the driver

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Full Solution:

Ernest has to know three other people, so if Bob can't know the Accessory, then Ernest is not the Accessory.

The Accessory was at the meeting and Bob will never know the Accessory, so Bob can't be at the meeting.

Damian knows only one person, so he can't be at the meeting. This means Albert, Charley and Ernest are all at the meeting as some combination of Driller, Driver and Accessory.

Damian knows only one person, so he can't be the Overlooker (who knows three)

Bob is the only other person not at the meeting, making him the Overlooker. Bob also then knows three people.

Damian will know the person who Bob (Overlooker) doesn't. Damian can't be the driver because he wasn't at the meeting.

Bob can't be the driver because he was not at the meeting.

Charley can't be the driver because she knows the driver.

Albert can't know three people, because it says he only knows two.

Albert knows ONLY two people, so he knows Charley and Ernest from the meeting.

Albert does NOT know Bob (Overlooker) or Damian (Hacker).

Bob knows three people because he's the Overlooker, but he doesn't know the >!Accessory so he knows: Driller, Driver and Hacker.

Bob knows three people because he's the Overlooker, but he doesn't know the Accessory so he knows: Driller, Driver and Hacker, which are Charley, Ernest and Damian (Hacker).

Charley isn't the driver, and can't be the Accessory, so she's the Driller.

This now makes Ernest the Driver by process of elimination.

And finally that makes Albert the Accessory.

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Assuming them knowing themselves doesn't count...

1. Given that the hacker is the only one knowing one person, and D is said to know the same number of people, D must be the hacker.

2. We know that D knows 1 person, A knows 2, and E 3. Assuming knowing people is mutual, the sum of the number of people everyone knows is even, so the sum for B and C must also be even. Neither can know only 1 person (either 0 or at least 2), and C knows the driver, meaning he knows 2, 3 or maybe even 4 people. B doesn't know the accessory, so he can know 0, 2 or 3 people.

3. Seeing as B won't know the accessory after the fact even though the latter definitely shows up at the meeting, it's safe to assume that B is the overlooker (who knows 3 people). Based on 2, C must also know 3 people.

A - knows 2 people
B - knows 3 people
C - knows 3 people
D - knows 1 person
E - knows 3 people

B, C and E must know each other, A knows 2 of the three and D knows 1 of them. A and D don't know each other. Since B already knows C and E, they can't be the accessory - it must be A. C isn't the driver, so he's the driller.

Who's who:

A - accessory, B - overlooker, C - driller, D - hacker, E - driver

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I hope I solved it right, being myself "only" 15yo.

Albert is accessory after the fact.
Bob is overlooker.
Ernest is driver.
Charley is driller.
Damien is hacker.

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