Logic question

[DarthMaximus]

@Bashir:

DM here is my solution:

1st house: Yellow, Civ, MIT, 40, Gold pen
2nd house: Blue, Mech, Purdue, 25, Template
3rd house: Red, Arch, GT, 50, T-square
4th house: White, Elec, TT, 30, Scale
5th house: Green, Indus, UCLA, 45 Compass

Which man attended UCLA?
The Industrial Engineer

Which has a gold plated drafting pen?
The Civilian Engineer

That is correct.  Good Job.

[Janus1]

ive seen this same problem, with different details. the punchline is: the german owns the zebra

[Avin]

Logic puzzles, huh?

How about something a bit more interesting?

Three perfect logicians, Alex, Bob, and Chuck, are sitting facing each other, and a fourth person puts a hat on each of their heads. On each hat, they are told, is some positive whole number, and one of those three numbers is the sum of the other two numbers. They can each see each other’s numbers but cannot see their own.

Alex says: I do not know what number is on my hat.
Bob then says: I do not know what number is on my hat.
Chuck then says: I do not know what number is on my hat.
Alex then says: The number 50 is on my hat.

He was correct! The question is: What were the other two numbers that Alex saw? Like DM, I will not accept random guesses of numbers: there is only one correct answer and you have to explain why that answer is correct and no other pair of numbers work.

(By the way, Maddogg’s puzzle was simple Algebra, I’m surprised it took so long! Three equations, three unknowns: S = 2(M-x), S-x = M, S = 24, solve for M)

[Note: edited to correct typo; see Maddogg’s post immediately below this]

[Guest]

….and 1 of those 3 numbers is the sum of the other 3 numbers ?? I think you need to get your act together Avin!!

[Guest]

Also, Alex declares " I do not know which number is on my hat", then does an about face and declares " the number 50 is on my hat" Is Alex a scitzophrenic or just a liar who you can’t trust? Get your act together Avin!!

[Yanny]

Zero and 50.

Course, that answer could be invalid based upon the definitions of whole and positive number.

[Avin]

Positive whole numbers generally exclude zero, as is the case here, as can be deduced even if it was uncertain on the basis that no answer is possible if zero is permissible (see my response to Maddogg). So no one has a zero, and furthermore everyone knows at the start that they cannot have a zero. This is critical to the problem.

Maddogg, regarding your first post, sorry, that was a typo. It should read the sum of the other two numbers. As for second post about Alex seeming to change his mind, that is the essence of the puzzle. At the beginning he did not know what number was on his hat, but after Bob and Chuck had spoken, he was able to determine his number. Therefore, even if zero was allowed, Yanny your answer would be incorrect because if he saw 0 and 50, Alex would have immediately known what number was his, but he didn’t.

[Guest]

Sounds like BS to me!

[Yanny]

Avin, question,

So, did Alex guess the number completely? Your wording confuses me.

But the only other situation I could think of would be if the other two hats were both 25.

[Avin]

Once again, the first time Alex spoke, he did not know what number was on his hat. Since he is a perfect logician, what that means is that he did not have enough information to determine what number was on his hat.

However, the second time Alex spoke, he did have enough information to determine that his number was 50. It was not a guess, he knew it for certain, given that Bob and Chuck were also perfect logicians. So their lack of knowledge about their hats must have told Alex enough to figure out what was on his own head.

So consider your suggestion of 25 and 25: if Alex saw that, then he could reason as follows: either my number plus 25 is equal to 25, or 25 plus 25 is equal to my number. Since the former cannot be the case because that means my hat is 0, then my hat must be 50.

However, Alex would have been able to apply this reasoning immediately: if he had seen 25 and 25, he would never have said that he did not know his number. Therefore, 25 and 25 is incorrect.

[Guest]

There’s something missing in the question. Otherwise it’s total nonsense!!

[Avin]

It’s possible I omitted something, but after rereading it, I don’t think so. The reason I liked this puzzle is that it seems like it shouldn’t have a unique solution, because it seems like you need more information, but everything necessary is there.

[DarthMaximus]

I have some guesses but I can’t really pin point it yet.  Long day.

Alex = A
Bob = B
Chuck = C

When Alex first looks he has two options for his number:  B+C or B-C

He has know way of knowing which is correct.

When Bob looks he also has two options, A+C or A-C, but not enough info to determine which one.

Now Chuck looks and also has two options, A+B or A-B, but can’t decide, however, this does give Alex the required information he needs to eliminate either B+C or B-C, thus he knows he has 50.

[Avin]

Keep it up, you’re on the right track, DM. Now you just have to figure out how Alex eliminates one of his two options (B+C or B-C) on his second “turn”.

I suggest you start by considering how someone would eliminate one of their two options without hearing anything from the other two people (which Yanny seems to have gotten), then how B might have eliminated one of his two options after hearing A’s first turn, then how C might have eliminated one of his two options after hearing both A and B, and finally solving the problem itself.

[Guest]

I think that the basic problem here is this. Alex knew immediately what numbers were on the other idiot’s hats. He learned nothing after that except……I don’t know what number is on my hat, from the other 2 goofballs. That wasn’t learning anything, because Alex already knew what was on their stupid hats. problem BOGUS

[Guest]

And another thing… How in the world could Alex deduce that his number was 50 when there was no more input from the other 2 idiots than " I don’t know what my number is"?? BOGUS

[Avin]

Sorry Maddogg, as you can see I indicated that DM was clearly on the right track. If you’re interested in trying to solve the problem, you might want to consider what he was saying and try to think about it more rather than just dismissing the problem as bogus. This problem is in some ways similar to the problem you posted in that it’s a word problem that yields a system of algebraic equations which, when solved, yields the correct answer. Unlike your problem though, this requires some abstract deductive reasoning, hence it being a logic puzzle, in order to arrive at the equations you need to solve.

[Guest]

BOGUS!!!

[DarthMaximus]

@MADDOGG:

BOGUS!!!

LMAO!!!

[Bashir]

@DarthMaximus:

Now Chuck looks and also has two options, A+B or A-B, but can’t decide, however, this does give Alex the required information he needs to eliminate either B+C or B-C, thus he knows he has 50.

He can eliminate B+C, because if A=B+C => B and C are both 25… He would have known immidietly…
So Alex knows it is B-C

So when Bob sees the hats the first time he sees 50 and C… He can’t make up out of that if it is B=50+C or B=50-C
Chuck also can’t make up his own number. He sees 50 and B… Hee can’t make up if it is C=50+B or C =50-B

Need to think about this…