## Friday, July 6, 2012

This puzzle is inspired by the recently ended Mad Men season 5 and is an interpretation of a puzzle from the Mathematical and Logical games book by Franco Agostini.

Don, Roger and Bert often meet and frequently drink together. We want to find out who had a drink at this particular client meeting. We know that:
1) If Don took a drink, so did Roger;
2) Roger or Bert frequently drink, but never at the same time during those meetings;
3) Don and Bert like to start such meetings with a drink, but not necessarily together;
4) If Bert drunk, so did Don.

Who had a drink on this specific occasion?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Anonymous said...

Maybe I am not thinking clearly here, but I feel as if this problem needs one additional piece of information to solve it: the name of one person who definitely had a drink at this meeting. None of the clues provide that detail, just relative relationships.

Clue 2 says that Roger and Bert often drink, but never at the same time during those meetings. Do they drink at different times during the same meeting or only drink at different meetings? I assumed the latter.

From Clue 1, we know that if Don drank, then Roger also did, but that (from Clue 2), Bert did not.

From Clue 4 and Clue 1, we know that if Bert drank, than so did Don and so did Roger. But with Clue 2, Roger and Bert do not drink at the same meeting, so therefore Bert did not have a drink.

Clue 3 just says that Don and Bert like to drink at meetings, not that they definitely drank at this particular meeting.

I feel stuck here.

Thanks,
TracyZ

Mai B. said...

Don and Roger both drank during the meeting.

Anonymous said...

Looking at the problem again, :)

I believe that based on the clues given, it is possible that either Roger or both Don and Roger had a drink at this particular meeting.

Bert did not have a drink (because if Bert has a drink then Don has a drink (clue 4), and if Don has a drink then Roger has a drink (clue 1), but Roger and Bert never drink at the same meeting (clue 2).

If Roger had a drink, then Don may or may not have had a drink.

TracyZ

anne-marie said...

All of them had a drink at this particular meeting.
Anah

anne-marie said...

Don, Roger, and Bert all drank in this meeting. At frst it said if don drank roger drank aswell and at the bottom it said if bert drank so did don. After i saw that i automaticle knew it was all of them. If one were to drink it would set of a chain reaction. EX: if bert took a drink don would to but if don took a drink so would roger sam way backwards or from the middle.

Sincerely, Ben

Jerome said...

I get five cases out of this.

Case One
========
Don Starts

Roger drinks because Don did, but we don't know when, just not at the beginning. Bert is not a certainty for case one.

Case Two
=========
Don Starts

Roger again drinks, although we're not certain when. This time Bert Starts right along with Don.

Case Three
==========
Bert Starts

Don drinks at the beginning (along with Bert). Because Don does, so does Roger, but he must do it during the meeting.

This looks pretty concrete to me.

Case Four
=========
Bert Starts

Don doesn't start with him. He drinks later. As soon as Don drinks, Roger follows.

Case Five
=========
Roger Starts
Bert follows sometime later. Don follows Bert.

The wording is a little tricky. Point three says not necessarily, which means you have to consider two possibilities.

Does this puzzle ask for just 1 answer? I'll consider whether there is one answer or not. If I do, I'll submit it later.

Anonymous said...

Okay this is my last post on this. :)

Per my earlier posts, I had determined that Bert did not drink at the meeting because if he did, and assuming Roger, Bert, and Don are all present at this particular meeting, then (based on clues 1 and 4) Roger would also drink which would mean that Bert couldn't drink without violating clue 2.

Clue 3 reads "Don and Bert like to start such meetings with a drink, but not necessarily together."

If this clue can be interpreted as meaning that either Don or/and Bert always start each meeting with a drink, then since Bert does not drink at meeting (per explanation above), then Don must be drinking.
(I had not interpreted it that way initially; my thinking was that even though they like to start the meeting with a drink, they might not have a drink at every single meeting.)

If Don has a drink then per clue 1, Roger has a drink.

So at this meeting, Don and Roger each have a drink, and Bert does not have a drink. Final answer. :)

TracyZ

Jerome's wife said...

The Question, "Who had a drink on this specific occasion?" is Bert. I am assuming that the question is asking for one specific person. I reasoned that Don and Roger are eliminated because they always drink together. Whereas, Roger and Bert frequently drink together and not at the same time, so therefore Roger is eliminated again because he always drinks with Don. Whereas, Don and Bert like to start the meeting with a drink, but not neccesarily at the same time, which I take to be that sometimes they do drink at the same time, but Don again is aliminated because he always drinks at the same time Roger drinks. The only person left then is Bert. So the answer is Bert

Ilya said...

Nothing certain can be concluded from (3), so it can be ignored.
Having studied the other three statements, I see that they don’t lead to a single possible outcome. One way to describe the logical possibilities is to call out letter combinations corresponding to first letter of the names of people who may have drunk. E.g. D means only Don drank while DRB means all three did.
* it’s possible that no one drank (“frequently” does not mean that it happened in this specific case)
* D - not possible because of 1
* R - possible
* B - not possible due to 4
* DR - possible
* DB - no possible because of 1
* RB - not possible because of 4 (or 2)
* DRB - not possible because of 2

So the possibilities are: no one drank, only Roger drank, Don and Roger drank

Annie said...

Bert cannot drink because if he drinks then both Don and Roger will drink and Roger and Bert don't drink together.

I would say Don and Roger. Roger could drink alone but Don likes to start meetings with a drink and if Don has a drink then Roger does too!

Maria said...

I think Ilya explained this in the clearest form. Out of all the combinations of drinkers the only possible ones are Roger or Roget and Don together. See Ilya's comment above.

A well-deserved puzzle point for everyone who dared to get into this logical mess.

Jerome said...

I don't mean to be argumentative, but I find leaving out the third clus should not be done. It adds a fuzzy notion to the problem which cannot be ignored. In fact it is what I used to answer as I did. It implies that right at the beginning of the meeting, either (or both) Bert and Don like to take a drink. So the cases one has to consider are

Bert starts the meeting with a drink
Don starts the meeting with a drink

or

Don AND Bert both take a drink at the beginning of the meeting.

The 4 clues are silent about what happens if Roger starts the meeting with a drink, other than saying that "frequently" Roger or Bert like a drink.

Talk about fuzzy. So if Roger starts, Burt may or may not follow, which leads to 2 other possibilities.

1. If Bert does follow Roger, then Don will take a drink as well

2. If Bert does not follow, then I think we are not certain what Don will do. There is nothing to tell what will happen under this circumstance.

Anyway, my point is that clue three is a monster and cannot be ignored. I don't think my first answer is correct by the way.

Maria said...

Jerome - I think the 3rd clue does not have a definite statement that either one of them drunk or not. Unlike other clues.
3) Don and Bert like to start such meetings with a drink, but not necessarily together;

However, I see your point that it does implies that either Don or Bert or both of them drunk. In this case, we can say that Roger and Don drinking is the correct answer and rule out Roger only drinking.