bonanova

Very nice!

Sergeant McGuffy remarked to his lieutenant one day after it was all over. "The way I reconstruct the crime, the innocent people were so excited when they first talked to us, they each got one fact wrong. But, the killer wanted to confuse our trail - and so coolly lied from beginning to end." Let's recap what we know ... Egmont VanDorn has been found dead in his apartment. From the beginning, it is pretty clear to the police that this was no accident. Before they can be separated, the four young people who found the body - Arnold, Betsy, Charles and Daisy - eagerly begin to tell their story. "If, as the police say, Egmont was injured between four and five," said Daisy, "that must let us all out. We were all together having dinner for at least two hours before we came over here." "But we all arrived at seven," Charles pointed out. "Arnold said that it was six o'clock at the time, just before we opened the door. Didn't you Arnold?" said Daisy. "I said it was just seven on the nose," said Arnold. "Sorry, honey." "I have no idea what he said or what time we got here," declared Betsy. "The thing I remember is the gas in the hall. We rang the doorbell, and no one came and no one came, and then I smelled the gas. My heart turned over, I thought to myself, he's dead. I just know he's dead." "Don't dramatize yourself," said Daisy coolly. "There is no way that you could have smelled the gas before we opened the door. The place was locked up, and sealed too, tighter than a drum. We'd still be in the hall if Eggy hadn't given me a key last week." "There was gas in the hall, all right," said Charles. "I smelled it before we opened the door. You seemed to take forever getting your key out. When you finally got the door opened, the gas just streamed out." "That was a pretty dangerous thing you did, Charles," said Arnold, "turning on the lights the way you did. Didn't it occur to you that a spark at the light switch could have blown us all up." "The lights were already on, Arnold," Charles replied. "For my part, I'm sorry about pulling him out of the oven - tampering with the evidence and all that," said Arnold. "Murder never crossed my mind. Locked room, you know. All I could think of was that maybe he was alive and we could still save him." "I don't believe this," said Daisy. "You didn't pull him out of the oven. I did. You ran and opened the window. Very good move, too, I thought at the time." "I opened the window!" cried Betsy. "I was dizzy from the fumes, and I knew I needed to do something fast." "The only things you opened were the door to the liquor cabinet and a bottle of Scotch, Betsy." Charles laughed at her. "And I thought they were good moves." "That was Arnold who got out the Scotch," said Betsy. "Don't you remember our sitting there after you called the police, and Arnold passing out the glasses?" "It couldn't have been me. Must have been you," said Arnold. "I've never been here before, I didn't even know where he kept the stuff. Charles, what did you do?" "Do you know what? I don't think I did anything. I remember quite clearly, walking over here with you after that long dinner we had together, and then seeing poor Eggy's feet through the door. But after that, I don't think I did a thing, except stand there gasping." OK it's time to make an arrest. Which liar done it?

Got another one? Welcome to the Den ....

To solve, we need to know if the first two picks were done [a] blindly or Monte Hall entered the room, looked into a bag unknown to us and removed a white marble, then went to another bag, unknown to us, looked inside and grabbed a black marble and then handed us the third bag and asks us now to guess its contents (calculate p of drawing white). I'm thinking we should assume it's [a] and go talk with *gulp* Professor Bayes. In that case an acceptable paraphrase of OP is: There are three bags (as described) someone grabbed a bag and with eyes closed pulled out a marble. It turned out to be white. Then he grabbed one of the other bags and pulled out, eyes closed, another marble. It turned out to be black. Setting those bags aside, we are handed the third bag and asked to say the probability of drawing white.

This probably does not need to be spoilered. These are the name lists I concluded. BABY: Amy Andrew Ann Jane Jason Jennifer Richard (Andrew Jason Richard are boy names) FATHER: Bob Chuck Gary George Jim Tom MOTHER: Betty Carol Judy Mary Susan Trudy LAST: Jacobs Larson Miller Smith Thompson Wilson

bhramarraj, we differ by an interpretation of OP, which is ambiguous. If "2 minutes" means "every 2 minutes" or "a particular 2-minute interval" the answer could be what jordge and I posted or your answer or anything in between. That is, in the second case the first pole is passed (sometime) in the first minute and the second pole is passed (sometime) during the second minute. That would permit your answer if pole 1 happened at the beginning of minute 1, and the second pole happened at the end of minute 2. Or am I missing something? So, is John Wilson still around to clarify?

Does "two of their sides the same" imply they are isosceles? Or that two sides of one triangle are equal to two of the other triangle's sides? It seems the latter, but thought I'd confirm.

OK maybe not all. How many pairs of mutually prime positive integers sum to 2x10250? You should be able to do this on the back of an envelope, and probably can't count the pairs with a simple program (before the earth freezes.) Pairs differing only in the order of addition count as 1 pair, not as 2 different pairs.

Which leads to the posts, #2 and #4, where the solution is given.

And that's all we need to solve.

OP says the accused is found guilty ( C ) if the action in question is defined as illegal (P) and the accused committed the action (Q) or in other words . That is implication: P and Q -> C. Do you mean if and only if? Or does it matter?

You're right - it's at least a 1/6 chance.

vigmester - nice solve. This is one of the better puzzles of the "find the fallacy" genre. Welcome to the Den!

Good solve. As far as I know this is the minimum number of moves (proven by simulation.)

Interesting puzzle. Clarify what happens when one switches and the other does not. What doe ending up with the same envelope mean: which one? Do they split the contents?