RAY: You have in your possession two pieces of string. Let's say that each is a couple of feet long, but it doesn't really matter. And they can both be different lengths, it doesn't matter either. And they're burnable, like the fuses that they use to, you know, light dynamite. Now you could light either end of either string, and it would burn. In fact, if you lit one end of a string, it would burn in exactly an hour. RAY: But here's the wrinkle: the strings do not burn in a constant, at a constant rate. For example, the string might burn for two minutes and then go crazy and burn like mad and then slow down, and da-da-da. You don't know what rate the string's burning at any specific time. All you know is that in an hour's time, the whole string is burned. It's not linear. RAY: So, the question very simply is, with the Zippo lighter and these two strings, how would you measure 15 minutes of time? RAY: Light three ends at once with the Zippo lighter. OK? RAY: So, you take String A, light both of its ends. You take String 2, and light one end. Well, what's going to happen? Because you lit both ends of the first string, in a half an hour's time, that string is going to burn up completely. RAY: A half an hour has gone by, and similarly, the other string you lit is going to burn for: half an hour's time. Right? RAY: At which point, as soon as the first string has burned up completely, you'll light the remaining end of String 2, and because the first part of that string you lit is continuing to burn, it's going to take 15 minutes before those two flame fronts meet, and you'll have measured exactly 15 minutes, Berman says... No, you'll have measured 15 minutes from the time that you lit the second string. ======================================================================= Ray: What man-made object first broke the sound barrier? Ray: Long before that--hundreds of years before that - the common whip. ===================================================================== Puzzler Answer: Tom Hoofs it Home Ray: Back in the old days when my brother used to work, my brother used to have his wife drive him to the train station and then he'd take the train and go to work. Then an hour later, he'd get on the train to come home. Tom: After lunch. Ray: Right after lunch. And he'd get to the train station and his wife would meet him there and they'd drive home. Well one day, he decides to leave work early at 11 am. Needless to say, he gets to the train station an hour early. Rather than call his wife, it's a nice day and he decides to hoof it. So he starts walking in the direction she'll be driving. And low and behold, he sees his wife coming up the road and she sees him by the side of the road taking a haircut. They get in the car and they drive home and arrive 20 minutes earlier. Don't forget - she left home at the usual time. Tom: Of course, she didn't know he was going to leave work an hour early. Ray: They get home 20 minutes earlier than they would have gotten home. How long was he walking before they met? Notice, there's no mention of how long she was driving, how fast he walked, what train he took, and what any other the distances were. How long was he walking before she picked him up? Tom: I got it. He was walking for 40 minutes. Ray: So close. Tom: Forty-five? Ray: Closer. Tom: Forty-six? Ray: Fifty. Because if they arrived home 20 mintues earlier than usual, he saved by walking 10 minutes of her travel time to the station and 10 minutes of her travel time from the station. Therefore, he was walking for 50 minutes when she picked him up. You have to put all of the pieces together. He left an hour earlier but she left at the same time and saves 20 minutes off the total trip. It's as if he moved the station 10 minutes closer. Tom: How did you get 50 minutes out of that? Ray: Ten minutes... Tom: Oh 10 and 50 is an hour! Ray: And 10 and 10 is what? Tom: Twenty! ===================================================================== RAY: Cool. Let's say you have two decks of playing cards, 52 cards each, regular cards. TOM: Yeah. RAY: And you put both decks together and shuffle them up. TOM: Got it. RAY: So, you've got 104 cards all shuffled together. Then you split them back into two equal piles. Well, you haven't looked at them now, in the traditional manner. You just counted them out so you have a pile of 52 on one side--we'll call that pile A--and a pile of 52 cards on the other side, and they're all mixed up. TOM: Pile 2. RAY: Pile 2. Here's the question: What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? And question 2, or B: How many cards do you have to look at to be sure of your answer? TOM: Yeah! RAY: Well? TOM: I happen to know the answer! It'sˇ RAY: Imagine! Go ahead. TOM: The chances are: one! RAY: Yeah, oh, 100 percent. TOM: One hundred percent. RAY: Imagine if youˇlet's say by some luck, you shuffled up all these cards and all the red cards wound up in one pile, we'll call that pile A. And for simplicity's sake, we'll call the other pile pile B, and all the black cards wound up in that. Then you would say, well, certainly the number of red cards in deck A, or pile A, equals the number of black cards in pile B. Now, I ask you to construct a scenario where it wouldn't be the case, always. TOM: How about one and 51? RAY: Exactly. Take a card out of pile A and donate it to pile B--but when you do that, you must reciprocate. TOM: Right. RAY: You must take a black card from pile B and donate it to pile A, and therefore you have 51 and one, and 51 and one, and no matter how you do this, if you wind up with 52 cards in each pile. ===================================================================== RAY: Well, here it is. My son was performing a common household task; something that each and every one of us has probably done many times. He asked me, Is 50 enough, Pa? I said, No, I don't think so. He said, How about 125? I said, No, I don't think that's enough either; I'd try 90. The question was, what household task was he performing where this would be true? I'd be willing to bet that most people, because our staff didn't have any clue, that most people don't know that this -- TOM: Our staff has no clue about anything. RAY: Oh, yeah, they can't find their feet in the shower. What he was doing, is that he was using the microwave oven. TOM: Oh, yes! RAY: Where 90 -- when you punch in 9, 0, start, is 90 seconds, which is a minute and 30 seconds. And it's more than 1,2,5, which is a minute and 25 seconds, not 125 seconds. TOM: No. Wow. RAY: So, there. Of course, there were doubting Thomases among us, including whom; my brother, Thomas. And -- TOM: No, I'm the one who ran over to the microwave to prove that you were right, because Dougie kept saying, No, no, if you put in 125 it's going to be 125 seconds. To which we said, Doug, I think you might be wrong about that. And indeed, when you put in 125, it reads it as a minute and 25 seconds. RAY: Yes. In fact, when it has counted off the last of the 25 seconds, it jumps to 59. ===================================================================== RAY: Maybe he's, maybe he wants to come out of retirement. There are three on-off light switches on the wall of the first floor of a building. One switch, one of the switches, one of the three controls a bulb in a lamp on the third floor of the building. The other two switches, like my brother and I, are disconnected. They're not connected to anything. TOM: They, they do nothing. RAY: Yeah. You're allowed to toggle the switches as many times as you want. Then you're allowed to walk just once, so you can do it, you can turn switches on one, you can turn all three of them on, you can turn all three of them off, you can turn two on, three on, one on, you can do whatever you want for as long as you want. Okay? Then you're allowed to walk just once to the third floor to check the light bulb. TOM: Right. And then you have to decide, which one of the switches on the first floor is in fact the one that turns the light bulb on or off. This is a great puzzler. Martin Gardiner is good. Especially considering that he's dead. RAY: Well here's the answer. TOM: Yeah. RAY: You turn the first switch on. You leave it on for ten minutes. Why, you ask? You'll see in a minute. Then you turn it off and you turn the second switch on and you go upstairs. TOM: And you leave the third switch in the off position. RAY: There you go. TOM: Yeah. RAY: If the bulb is on, then it's switch number two, which is the one that's on. TOM: Right. RAY: OK? If the bulb is off and it's cold, then it's switch number three, which is the one you never touched, that controls that light. If the bulb is off but it's hot, then it was switch number one. ===================================================================== Many years ago a prisoner was condemned to die. He was in his cell, and the warden came to visit him. He said to the prisoner that his odds of dying the next day are 100% ( Big damn surprise, right?) But the warden wants to increase the prisoner's chances to 50%. The warden gives the prisoner 2 shoeboxes, one with 50 white marbles, and one with 50 black marbles. The warden will come in blindfoldeed and pick a marble out of one of the boxes. White, he lives. Black, he dies. The marbles can be arranged in any way. All the marbles must be used in either box. Is there any way to improve his chances above 50%? The Prisoner's dilemma: The prisoner can improve his chances from 50/50. If he rearranges the marbles, putting 99 marbles in one box and 1 white marble in the other box, his chances are improved. ===================================================================== RAY: Exactly. It was a dark and stormy night. The location is a secret airfield somewhere in England during WW, WW 2. TOM: The big one. RAY: The RAF had summoned one of England's most noted mathematicians to help them solve a problem. I think I mentioned he will remain nameless, because no one... Anyway, they were having a problem as I am sure most people were aware, because they were attempting to bomb Germany, and the German anti-aircraft fire based on the ground was inflicting heavy losses on the Brits. And their planes are being shot down right and left and the ARF they have to do something to diminish their losses. Now clearly they could put armor plating on the bottoms of the fuselages and the wings, but there were several problems that came along with this. One, they would have to become ground based planes, because they wouldn't be able to fly. The ones that could would have their range considerably reduced, and of course, their ability to carry cargo and bombs and fuel and whatever would be diminished because of this additional weight. TOM: Yeah. So, they had to be very selective. If they were going to put any armor -- RAY: At all. They had to be selective. TOM: Be very, very selective. RAY: Anyway, so this nameless mathematician crawls underneath the planes and looks at where the bullet holes are underneath them. Now there were bullet holes all over the place as you might expect. In the wings and the fuselage and seemingly distributed randomly on the undersides of these planes. He studies hundreds of planes, takes pictures, draws things and whatever and then he makes his recommendation. The question very simply is, what armor plating, if any, does he recommend putting on these planes, and why? RAY: It will get shot off. You'll never fly. Well, what he noticed was that the planes that returned, the surviving planes, indeed had bullet holes all over the place, but he figured that the ones that didn't return had bullet holes where these planes didn't have bullet holes. RAY: So, what his recommendation very simply was, armor plate the unhit areas that the returning or surviving planes had in common. When he surveyed the undersides of these, he noticed that there were a few spots that all of them had in common that had no bullet holes. And he had to assume that the ones that hadn't returned had -- ===================================================================== RAY: Now, here's the puzzler. Suppose a mother has two kids and not the older one, but just one of them is a boy, what are the chances that the other one is also a boy? TOM: Phew. RAY: Now if you draw little pictures. There are four possible scenarios. TOM: Yeah. RAY: Older boy, younger boy. We'll call that B and B. Older boy, younger girl. Older girl, younger boy. TOM: Um hmm. Yeah. RAY: And older girl, younger girl. That's it. If you're going to have two kids, that's it. All right? Now, in the first case -- TOM: Of course. RAY: If I say... When I say the older one is a boy -- TOM: Um hmm. RAY: That it immediately leaves out the last two -- TOM: Exactly. RAY: Possibilities. TOM: That's right. RAY: OK? It can only be boy-boy or boy-girl. TOM: That's right. RAY: Right. So, in order for it for the other one to be a boy, it's a 50-50 chance. TOM: Right. You can have boy-boy, boy-girl. RAY: Right. Or, now... Now! TOM: Yeah. RAY: When I say that one of them is a boy, I believe... Believe it or not it is this counterintuitive -- TOM: It certainly is. RAY: It becomes harder for the other one to become a boy. TOM: Um hmm. RAY: And the chances are one in three cause if you look at the scenarios, you have boy-boy, boy-girl and girl-boy. TOM: Sure. RAY: Right? For the other one to be a boy, it's gotta be choice #1 which is boy-boy cause you already said that one of them is a boy, how can the other one be a boy? There's one chance in three. Hard to believe. Isn't it? ===================================================================== RAY: And of course Dougie too. Here it is. Simply the following polynomial or in other words tell me the product of the following string of terms. Here they are. In parentheses, (x+a) times in parentheses (x-b) times in parentheses (x+c). You get the trend here? TOM: Yeah. RAY: Da, da, da, da, da. TOM: X minus d, x+e. RAY: Right, times -- the last term is x-z. TOM: Got it. RAY: And...the answer is if you go back two terms, the previous term -- the last letters of the alphabet are z, y, and x in reversed order. So it would be x+y and the term before that would be x-x. TOM: Oh, Sonia ?? ===================================================================== RAY: As briefly as I can. Everyone remembers the game show, Let's Make a Deal, where the contestant was presented with three doors, Door Number One, Number Two, and Number Three. OK. TOM: Yeah. RAY: Behind one of the doors is a wonderful prize and behind the other two doors were crummy prizes, known as zonks. OK? TOM: Yeah. I got it. RAY: Here's the puzzler. You are the contestant. Monty Hall says, "Pick a door." Go ahead, pick a door. TOM: Three. RAY: No, you have to pick two. TOM: Two. RAY: OK. Monty Hall says, "OK. You've picked Door Number Two." Now, in the real game, he offered you cash, whatever. We simplified it. TOM: Yeah. RAY: He says, "I'm going to show you what's behind one of the doors that you didn't pick." Now, because there's only one prize needless to say, I won't even say it, those two doors have one, either two zonks -- TOM: Or one prize and one zonk. RAY: Right. TOM: Yeah. RAY: And those are the only choices. TOM: Yeah. RAY: OK. TOM: And I'm going to show you what's behind one of the doors. RAY: So, he knows where the zonks are. So, he says, "I'm going to show you what's behind Door Number One" and he shows you that, '63 Dart. He then says, "Do you want to switch your choice from Door Number Two to Door Number Three?" And your logic is what? TOM: What's the difference? RAY: What's the difference? I had a one in three chance of winning before. TOM: Right. I could have just as easily have chosen Three the first time. What's the difference? I'm sticking with Two. RAY: And that's the answer you should stick. It's a stupid puzzler. No, that isn't the answer. The answer is you should switch. Now, I know this is going to generate all kinds of gnashing of teeth and all kinds of controversy and -- TOM: Oh, especially among all the college professors who've been teaching probability theory, all their lives and think they understand it. RAY: Well, I know I don't understand anything. TOM: I was one of them. RAY: You should switch because if you don't switch, your chance of winning is one in three. We already know that. You just pick a door. No matter what he does, your chance is one in three. TOM: Exactly. RAY: If you do switch, this is the part that's hard to believe. Your chances become two in three. You double your chance. TOM: Impossible. I can hear it all over the country. I can hear them all. RAY: And hear it reverberating. TOM: Impossible. RAY: From sea to shining sea. TOM: The guy's so blimped out now, they've gone over the edge. I won't stand for it. What's their e-mail address? RAY: From Springfield to Springfield to Springfield. TOM: To Fairview to Fairview to Fairview. RAY: Here's the simplest way I can explain it. What Monty Hall is basically offering you is this, he says, "You've chosen Door Number Two. Would you like to switch for Doors One and Three?" TOM: Exactly. RAY: Because he knows where the zonk is he's obviously going to show you the other zonk which is Door Number One and, but he can't show you Door Number Three because the prize might be there. TOM: It might be. RAY: And if it is there, he can't show you that so, what he's basically saying is "You pick Door Number Two. I'm going to give you One and Three." TOM: If he had not shown you what was behind Door Number One and simply said -- RAY: Would you like... TOM: Would you like to switch from Door Two to Doors One and Three, would you always switch. Of course, you would. RAY: Right. And if he said to you, if you showed you nothing and asked if you would switch from Door Number Two, your answer would be no, but because he has shown you one of the zonks. TOM: Now, you believe that it doesn't matter. ===================================================================== RAY: Adrienne. I don't remember the spelling, but if it's Adrienne, it's certainly a woman. Here it is. I didn't change much. The beautiful young princess had a dilemma. She was in love. TOM: Now, you think I didn't remember this. RAY: I knew you remembered. Of course, I did. She was in love with Igor, a blacksmith's son and a hunchback, but she wanted to marry him anyway. However, she knew that her father, the King, would not approve. Moreover if the King knew of their love, he would surely have the young man executed. Wouldn't he? TOM: Yeah. RAY: They devise a plan. They will elope. Aha! Pretty good, huh. TOM: Yeah. RAY: Old plan, but sometimes works. Sadly, their plan is foiled and they are stopped at the castle gate by the guards who spotted Igor's hump. And they are brought before the King. TOM: Yeah. RAY: Now, the King was indeed furious, but he decided to offer Igor a sporting chance. TOM: Yeah. Just to make it look good, it turns out. RAY: He said he would take two pieces of paper and write the word, princess on one piece and Dodge Dart. I mean death on the other and the young lad could decide his own fate by selecting one of the slips of paper from a jar. TOM: Yeah. RAY: The two slips of paper are crumpled up and thrown into an olive jar and young Igor has his fate in his own hands. TOM: Um. RAY: If he picks princess, he gets the princess. Death, he gets the Dart. However, he knows that the King is sneaky and the King writes death on both pieces of paper. TOM: Oh. RAY: But despite this, despite this, Igor manages to win the princess' hand. How does he manage this? TOM: Wow! This is good. RAY: Historic folklore. TOM: Any story with a hump in it is good. RAY: He reaches into the jar. He pulls out a crumpled piece of paper. He uncrumples it. TOM: Yeah. RAY: And he reads on it, death. A big smile comes across his face. TOM: Guy's a quick thinker. RAY: He immediately stuffs the piece of paper in his mouth, chews it and swallows it. TOM: Right. RAY: Dances around the room and says, "Oh my God, I can't believe my good fortune." And everyone says, "What did it say?" He says, "Ask the King what it says on his slip of paper and you'll know what mine said." TOM: Oh, ho-ho-ho. What mine said. RAY: The King don't want it to be revealed as a duplicate, sneaking liar that he is has to show the piece of paper. TOM: Shoves the paper in his mouth and swallows it. RAY: Wasn't thinking quickly enough to do it. Shows his piece of paper that says, death. TOM: It says death. RAY: Dodge Dart. TOM: So, the other one must have said, "the princess." ===================================================================== RAY: In 1918 a man was arrested for a crime and sentenced to life in prison. Thirty years later, with the help of a friend, they concoct an escape plan. And very simply, the friend was to leave a get-away car in the field near the prison -- and the guy is going to dig a tunnel or climb the wall or bribe a guard -- I don't know what he's going to do. Anyway, the escape goes like clockwork. The convict finds the get-away car just where his friend said it would be and all he has to do is get in the car and drive away. But he can't start the car. There's nothing wrong with the car, and by the time he figures out it -- they're what? TOM: On him. RAY: Putting the cuffs on him with the dogs and the whole bit and making plans to exile him to New Jersey... TOM: I've got the answer to this one too. His friend forgot to leave the key because he was afraid someone would steal the car. RAY: Well.... TOM: It was a bad neighborhood. Well we know that already. RAY: Of course. If the prison's there it must be a bad neighborhood. TOM: Yeah. RAY: No, his friend left the key and that is, in fact, the answer. TOM: That was the problem. Yeah. RAY: When he went to jail, cars didn't have electric starters -- cars had cranks. He gets there, he finds the car, he's not looking for a key... TOM: He's looking for the crank. RAY: The crank. And he's trying to figure out "where do I crank up the car?" Because in the intervening thirty years they had made this wonderful advancement in automotive technology that allowed people to get in and turn a key and step on a starter switch and he didn't know about this and while he's fidgeting around, and futzing around trying to figure out how to get the get-away going...they slap the cuffs on him. TOM: The guards come. ===================================================================== TOM: Is it time for the puzzler about the blind guy? RAY: So you know, I was going to suggest, today, that you ask me what the puzzler is. TOM: Well you know, if you didn't have your little piece of paper there, I wonder if you'd remember yourself? RAY: Well, as I was driving in, I turned off the radio and I couldn't. TOM: See? RAY: All right. TOM: So? What is the puzzler? Do you remember? RAY: No. I have to get my notes. All right, here it is. TOM: Yeah. RAY: A major league umpire enters the subway by walking down the stairs with the assistance of his seeing eye dog. TOM: Uh oh. You are going to get nasty mail from all the major league umpires now. RAY: Do you know? TOM: Matter of trivia... RAY: It wasn't until 1966 that a major league umpire wore glasses. TOM: No kidding? Up until that time they were afraid to? Because everyone was always yelling 'Hey! What do you need? Glasses?' RAY: Right. TOM: And finally said 'Geesh, you know I do!' RAY: Finally one brave soul wore his glasses and he escorted all the umpires to their positions from that point on. TOM: Yeah. OK. So? RAY: Anyway, so this major league blind umpire goes into the subway station. TOM: Right. With his seeing eye dog. RAY: In fact, he had just come from Yankee Stadium where he had worked an afternoon double-header behind the plate. Anyway the dog leads him to the bottom of the stairs at the subway station where he arrives at a cage, behind which is sitting a woman who is the token vendor. Right? Are you with me so far? TOM: She was the token vendor? Not the token vendor -- you mean the vendor of tokens. I mean I'm usually the token Italian wherever I go. RAY: And there's a sign below the window that says 'Tokens - 40 cents.' TOM: Um hmmm. RAY: The dog pees on the sign while the guy rummages around in his pocket and through the slit in the cage he hands her a dollar. TOM: Yeah. RAY: No words are spoken. TOM: Of course not. RAY: No gestures are exchanged. TOM: Oh! RAY: No little notes handed between them. TOM: No. RAY: She has never seen him before and he obviously has never seen her before. TOM: Yeah. RAY: She hands him two tokens and 20 cents change. The question is very simply, how did she know he wanted two tokens and not one? TOM: Is the dog involved? RAY: The dog is not involved. TOM: Is the fact that he is blind involved? RAY: Only tangentially. TOM: Oh! RAY: That was in the way of a hint. TOM: Oh! RAY: A very small hint. TOM: Everything counts. RAY: Yeah. Very small hint. And the answer, very simply, is, that he didn't give her a dollar bill, he gave her, in fact, four quarters. TOM: So simple. RAY: So simple. Of course if he had given her four quarters he'd wanted two tokens otherwise he would have given her two quarters for which he would have received one token and a dime change. ===================================================================== Ray: All right. Well, here it is. What do the following men have in common? Ulysses S. Grant, Rudyard Kipling, Woodrow Wilson, Grover Cleveland, and Calvin Coolidge. Now we know they're all dead. And they do have certainly that in common. What do they have in common other than the fact that they are all famous and that they're all dead? Tom: I don't know. Ray: You dont know? Well, they are best known by their middle names. Tom: What? Ray: Yes. Tom: Ulysses S.? Sam? Ray: No, no. Tom: Ulysses is not his first name? Ray: His real name was Hiram Ulysses Grant. He added the "S" for Simpson later on in life. Tom: Oh. Ray: Joseph Rudyard Kipling, Thomas Woodrow Wilson -- you knew that because that was a trivia question that you may have used on the web site at one point or another. Stephen Grover Cleveland and John Calvin Coolidge. ===================================================================== Ray: Anyway, where was I? The moon can go between us and the sun and block out the sun and if they didn't appear to be the same size we wouldn't have an eclipse. Now, knowing this, you can take the tip of your finger and at arms length you close one eye and you can block out the sun with the tip of your index finger. NO - not that finger! The other finger! Now, I wouldn't try this because according to Tony's mother you can go blind if you do this! However, you go out at night and you hold that same finger up and close one eye and you can't block out the moon. How come? Here's the answer: Because during the day, when you look at the sun, your pupil shrinks because of the sunlight. But at night, your pupil dilates to absorb more light, so your pupil actually looks around the tip of your finger.