Can you spot the fallacy?

[Mike Simmons]

Tim Holloway wrote:As a measure of programming aptitude it fails, because one of the first things you want to do when solving a problem is to obtain as much data as possible. But this puzzle is predicated on the absence of something, not its presence.

This attitude still makes no sense to me. Have you never had to debug a problem where you didn't know what had happened, but could eliminate some possibilities by the absence of certain log entries? It shouldn't be considered rocket science to figure out that silence can transmit information.

FWIW, I don't think it's a very good interview question either. Certainly not as a single question with everything riding on it. But as one small part of a much larger interview, with a good interviewer who can adapt the question to a discussion format (which the interviewee should do anyway) to get an idea how a person thinks... well, it's still not a great question. But they could get some value out of it. Perhaps moreso for an entry-level position where candidates don't have a standard level of knowledge expected of them, or for a job role that requires thinking outside the box.

[Mike Simmons]

Mike Okri wrote:The only problem I have with the puzzle is that C cannot be 100% certain of the color of his hat. He can only be reasonably certain.

Agreed. And in an interview setting, this is a good thing to bring up, along with the other assumptions that would be required to make it 100%. But none of that needs to prevent a candidate from obtaining a reasonably good answer.

[Tim Holloway]

I don't know how much "out of the box" this is. My definition of out-of-the-box tends to be a lot further out than that. Which is where stuff like D being a suicidal sadist come into play.

However, I believe that - taking the implicit communication into account - C can be 100% certain. Since there are only 2 hats of each color and only 2 colors, either B and C will have the same color or they will not. B's color is visible to C. Therefore if D says he's wearing White and C sees a black hat on B, it's because D knows that the 2 black hats are on B and C, both of whom are visible. And conversely, if D says he's wearing Black but B's hat is white. Only in the case where B and C are not the same color will D be uncertain and remain mute. Assuming everything goes according to the theoretical rules and none of the real-world exceptions we're discussed apply.

[Mike Simmons]

Tim Holloway wrote:However, I believe that - taking the implicit communication into account - C can be 100% certain. [...] Assuming everything goes according to the theoretical rules and none of the real-world exceptions we're discussed apply.

Well, that's the rub. Those things weren't stated, so I'd argue C's not 100% certain. I've argued C should still act, without that certainty. But he can't be 100% certain without those unstated assumptions.

Here's another one: how much time does C need to achieve this alleged 100% certainty? If the deadline is in 10 minutes, and it's a life-and-death situation, isn't it possible D's silence is just because he's weighing options, making sure he hasn't made a mistake? Alternately, would 10 seconds have been enough? How about 1 second? What's the cutoff for achieving 100% certainty here?

[Tim Holloway]

Mike Simmons wrote:

Tim Holloway wrote:However, I believe that - taking the implicit communication into account - C can be 100% certain. [...] Assuming everything goes according to the theoretical rules and none of the real-world exceptions we're discussed apply.

Well, that's the rub. Those things weren't stated, so I'd argue C's not 100% certain. I've argued C should still act, without that certainty. But he can't be 100% certain without those unstated assumptions.

Here's another one: how much time does C need to achieve this alleged 100% certainty? If the deadline is in 10 minutes, and it's a life-and-death situation, isn't it possible D's silence is just because he's weighing options, making sure he hasn't made a mistake? Alternately, would 10 seconds have been enough? How about 1 second? What's the cutoff for achieving 100% certainty here?

Which is where the trickery comes in. The entirety of the puzzle tells you that none of the above happened - C deduced the answer after 1 second and didn't get shot. The puzzle therefore consists both of the specifications of the puzzle and the meta-information which appears to follow the puzzle, but is in fact, part of the puzzle.

[Mike Okri]

Tim Holloway wrote:I don't know how much "out of the box" this is.

I'm pretty sure that a puzzle like this is not designed for people of your calibre. I'm sure that a puzzle like this is designed to test whether a young programmer has the potential to blossom into a senior programmer with strong analytical skills. This puzzle will test whether he is clever enough to realize that lack of information is information. Not many young programmers are able to do this.

[Tim Holloway]

Mike Okri wrote:

Tim Holloway wrote:I don't know how much "out of the box" this is.

I'm pretty sure that a puzzle like this is not designed for people of your calibre. I'm sure that a puzzle like this is designed to test whether a young programmer has the potential to blossom into a senior programmer with strong analytical skills. This puzzle will test whether he is clever enough to realize that lack of information is information. Not many young programmers are able to do this.

I wouldn't count in it. Doing it was what got me into trouble when I was a young twerp.

It still gets me into trouble. The boss gets angry and say "Just Git 'er Dun!"

[Matthew Brown]

Bear Bibeault wrote:I'll disagree on both counts. I would not have been able to come up with the answer, and I think I'm reasonably intelligent, and few people I've worked with find me a nightmare to work with. In fact, many jobs have been with former coworkers who wanted to work with me again.

I was being flippant, I admit. But I'll also admit to being a little surprised. Maybe it's because I am familiar with questions like this, but I thought it was fairly obvious what the problem was intended to be, even if it's possible to tear apart precisely how it was stated (as has been demonstrated). And once you know what the problem is intended to be, I don't think it's all that difficult.

So what I was really talking about was someone who understands precisely what they meant, and knows the solution, but still refuses to cooperate. I can be as pedantic as the next person...but I'd never dream of doing it in an interview! Precise, yes, not pedantic. And I think there's a middle ground of answering the question as intended while pointing out the flaws, if you insist on doing that.

[Bert Bates]

When I'm interviewing, I don't rely on any single line of questioning. So such a puzzle "could" demonstrate a candidate's ability for lateral thinking. But I would never make or break a candidate because of one puzzle - it's just more data...