Batman would, in the first minute, lick the stripes of four boxes: A, B, C, and D. In the second minute, he would lick the stripes on boxes E, F, G, and H.

Meanwhile, as Batman gets his first licks in (as it were) in the first minute, Batgirl would lick the stripes of boxes C, D, E, and F. In the second minute, she would lick the stripes on G, H, A, and B.

Now, in the first minute, Robin would lick boxes A, F, C, and H. In the second minute, he would lick B, E, D, and G.

That way, we get the following eight scenarios:

In case of A being the box containing the antidote, Batman and Robin's tongues would go numb after 3 minutes, Batgirl's after 4. (Batman 3, Batgirl 4, Robin 3)
In case of B: Batman's after 3 minutes, Batgirl and Robin's after 4. (Batman 3, Batgirl 4, Robin 4)
In case of C: Batman 3, Batgirl 3, Robin 3
In case of D: Batman 3, Batgirl 3, Robin 4
In case of E: Batman 4, Batgirl 3, Robin 4
In case of F: Batman 4, Batgirl 3, Robin 3
In case of G: Batman 4, Batgirl 4, Robin 4
In case of H: Batman 4, Batgirl 4, Robin 3

Am I warm?

A-ha! Oh well, I tried! But I'll never be a Batman-level detective.

I'm a few weeks late with the answer; here it is:

RAY: Why does he go to the first barbershop, the one that was messy, and disgusting, where the barber had a lousy haircut? He goes there because it's clear that each barber gives the other one his haircut. So the guy that has the great haircut is getting it from the slob.


And the two Puzzlers that have happened in the meantime:


1. RAY: Pick out a three digit number and write it down. Now, repeat those three digits. So, if you picked 2-7-1, you now have 271271. Now I want you to divide that number by seven.

Now, if you have a remainder, put it off to the side. Like if the remainder's one, two, whatever it is, put it off to the side. Take the quotient that you got and divide that by 11. And whatever remainder you have, put that off to the side too.

TOM: Got it, yeah.

RAY: Now, divide that remaining quotient, the quotient you just got, by thirteen. Another prime number! OK, now take that number that you've got, and the quotients, the remainders that you had from the previous divisions, and add them all together.

TOM: Add what together?

RAY: Add the remainders and the last quotient that you got. And you're going to wind up with the original number. So, the question is, why does this work?



2. RAY: The warden admits three prisoners into his chambers. He tells them, "One of you fellas is going to have a chance to get out. Here's the deal.

"I'm going to blindfold all of you, then I'm going to put hats on your heads. I have three white hats and two black hats. Each of you is going to get a hat. You have to figure out which color hat you have to get released."

He blindfolds them and puts a hat on each prisoner. They're led out of the room in single file. When the blindfolds are removed, the guy in the back can see the two people in front of him, the guy in the middle can see the one guy in front of him, and the guy in front can see nobody.

TOM: They can't turn around? They have to walk around the prison in this order?

RAY: Right. And they walk around the prison, stopping outside the warden's office. The warden says to the fellow in back, who can see the two people in front of him, and their hats, "Can you tell me what color your hat is?

Don't forget, there are three white hats and two black hats available. The fellow in back says nothing. He doesn't know.

The fellow in the middle is asked the same question. He is unable to answer.

The guy in the very front, who can see no hats, knows. He says, "I can identify the color of my hat."

How does he know?

I think number 1 comes down to the fact that because of the way the 6-digit number is defined, it can be written as 1001n, where n = the initial 3-digit number given, and then 1001 can be factored down to 7x11x13.

So when you divide the 6-digit number successively by 7, then by 11, then by 13, your last quotient should be n and the remainder(s) 0.

Ish, that's a link to this thread.

We have two smart people here, they figured it out. Here are the answers:


1. RAY: When you take a number like 1, 2, 3, or 4, 5, 6, or 7, 2, 1, and multiply it by a thousand and one, you wind up with the same number repeated. So if you start with 4, 5, 6, and multiply that by 1,001, you get 4, 5, 6, 4, 5, 6, don't you? And then all you're doing now is dividing it by the factors of 1,001. Which happen to be, some of which happen to be, 7, 11, and 13. So I knew you weren't going to come out with any remainders.

TOM: You little devil, you.

RAY: And that's the reason it works, no matter what the three numbers are.



2. TOM: His hat was white. He knew because the other two guys didn't know what color hats they were each wearing.

RAY: That's right. Because the back prisoner said nothing, he must have seen either two white hats or a black and a white hat in front of him.

Now, if the prisoner in the middle had seen a black hat in front of him, he would have known that he was wearing a white hat. Why's that? Because if he had a black hat on, then the guy who was in the back would have known that his own hat was white, and he would have spoken up when he had his chance.

Because the prisoner in the back and the middle didn't say anything, then the prisoner in the front knew he had a white hat.


And this week's Puzzler:

RAY: A woman and her husband decide to go shopping one Saturday for a used car. So they go to the neighborhood used-car dealer and a young man is shows them the various cars in the lot.

They don't seem to be really excited about any one of them. Finally, the used-car dealer says, "Oh, how could I have forgotten this one? I have just the car for you. I know you are going to love it."

He takes them over to a late model Japanese car. "You're not going to believe this. This car belonged to my fourth-grade teacher, Ms. Johnson. It's a wonderful car, and she treated it very well, and had all the service done here. Interestingly, she never left town with the car. All she ever did with the car was drive from home to school and back, and on Sundays she went to church. She never used the car on Saturdays."

They look over the car and it looks magnificent. So the woman asks the obvious question: "Why did Ms. Johnson sell the car?"

"Well, as luck would have it,' he says, 'She was called out of town on very short notice to care for a sick relative in the Midwest so she came in here last week and sold us the car, and of course, it's your good fortune that it's here."

The woman gets in behind the wheel, and starts up the engine. It sounds fine. The husband sits in the passenger seat and they fiddle with the controls. She fiddles with the controls on the dashboard, tries the wipers, blows the horn, and looks around the car.

"Geez, honey," her husband says, "It's a great color, too. I think we ought to get it."

"I don't think so," she says, as she turns off the key. "He's lying to us."

The question is, how did she know? (The answer is not that the salesman was moving his lips.)

Is it that used car lots don't service vehicles?