[Vortex]

Originally posted by Sesquipedalian


We have a winner!  Your logic reasoned in the opposite (and harder) direction from what I did to solve that puzzle, but it worked.

My easy explanation for anyone interested:

1) If none of Betty, Cindy, or Debbie were wearing a blue hat, Alice would know she must be wearing a blue, but she does not know, so one of the other three must be.  

2) Therefore, Betty knows that at least one among herself and the girls in front of her are wearing blue.  If neither of the girls in front of her were wearing blue, she would know she was wearing blue, but she does not know, so at least one of Cindy and Debbie must be wearing blue.

3) Therefore, Cindy knows that if Debbie is not wearing blue that she must be, but she does not know what she is wearing, so Debbie must be wearing blue.

*Vortex receives a cookie*

Oh man, your reasoning is definitely a lot easier.

[Sandwich]

Originally posted by Goober5000
Any other good brain teasers?

Yup:
[q]
The Paycheck Puzzle
Mr. Brown gave his gardener a check in full payment for some extra work. The check was in three figures and actually was more than the gardener was owed, so he was very pleased.

"Just a minute," said Mr. Brown. "If you will not cash the check, I will give you the difference between the product of the three figures showing the dollars, and their sum. I can tell you that this is not a small number.

The gardener agreed to this apparently generous offer, but was very disappointed when he learned the truth of the matter. How many dollars was the check made out for?[/q]


Good luck!

[Vortex]

Um... well I guess $100 wouldn't give you too much...

[Sandwich]

No, but the difference would be $1, which is a small number.

[Vortex]

Ah ok, well then what do you define as a small number though? Would -100 be considered small (it is rather large scalar wise).

[Sandwich]

For the purposes of this teaser, let's just say that the difference is not a negative number.

[Blue Lion]

$123

[Sandwich]

Originally posted by Blue Lion
$123

Whoah! *tosses BL a peanut-butter and chocholate cookie*

How'd ya figure it out?

[Blue Lion]

I knew it was a trick question. Just the way it was worded tipped me off there was no difference between the product and the sum.

1+2+3=6

1*2*3=6

And I'd hit that guy for calling 0 "not a small number"

[Sandwich]

Whoops, how'd this slip down so far?? Here's another one:

The Three Small Boys

Three small boys were talking together when they were joined by an older man. The newcomer noticed that each of the threee boys had a smudge of dirt on his forehead.

"Boys," he said, "will each of you look at the foreheads of the other two and if you see a smudge of dirt on either or both, raise your hand." All three boys looked and all three raised their hands.

"Now," said the old gentleman, "if one of you is certain that he has dirt on his own forehead and can tell me how and why he knows this, he is to raise his hand and I will give him a quarter."

The three boys looked at each other for a few moments, and one of them suddenly raised his hand. Can you figure out how he knew that he had a smudge on his forehead?

[Blue Lion]

One of his brothers was wearing glasses

[Joey_21]

nevermind

[Kamikaze]

I'm putting what I got in black

None raised their hand for a while, that implies all three saw a mark on each other boy. (because they each thought they may or may not have a mark, because at least two have to have a mark. If only one other person had a mark they would know they have a mark) Therefore the boy deduced that and raised their hand.

of course this depends on the other boys thinking this way and being relatively intelligent...


that's all I could come up with

[Blue Lion]

It was ash wednesday

[Goober5000]

Suppose boy A didn't have a smudge.  He sees the two other boys B and C have a smudge.  Now suppose you take B's POV.  B sees C with a smudge and A without, and C is raising his hand.  This means that C sees a smudge, but since A doesn't have a smudge, this would have to mean that B has a smudge.  B would instantly realize this and give the answer immediately, since it's pretty obvious.  The same goes for C.

Since neither B or C gave the answer right away, this must mean that A in fact actually does have a smudge. QED (or not...)

[Blue Lion]

Originally posted by Sandwich
The newcomer noticed that each of the threee boys had a smudge of dirt on his forehead.

[Kamikaze]

Blue Lion, he's implying that it can't be that only two have smudges because of the response times of two of the people.... not that only two have smudges

[Blue Lion]

o.O misread that.

[Joey_21]

Originally posted by Goober5000
Suppose boy A didn't have a smudge.  He sees the two other boys B and C have a smudge.  Now suppose you take B's POV.  B sees C with a smudge and A without, and C is raising his hand.  This means that C sees a smudge, but since A doesn't have a smudge, this would have to mean that B has a smudge.  B would instantly realize this and give the answer immediately, since it's pretty obvious.  The same goes for C.

Since neither B or C gave the answer right away, this must mean that A in fact actually does have a smudge. QED (or not...)

That was just about what I had posted.

[Goober5000]

Yeah - hypothetically, *if* A didn't have a smudge, then either B or C (or both) would give the answer immediately.  Since A sees that both B and see have smudges, and neither answered immediately, then that means A *does* have a smudge.

Admittedly, the wording of the solution is confusing.  It's easier to visualize.  Try drawing three circles on a piece of paper, then pretend that one of the circles is imagining what one of the other circles is seeing.

EDIT:

Originally posted by Joey_21


That was just about what I had posted.

Then you should have kept it!  Nothing ventured, nothing gained.