bonanova

This may have been posted before in this forum, and the solution I posted then had a slight violation. It's an interesting puzzle because it takes only one move look ahead to find wrong moves. Most moves are immediately dictated.

Well now, don't that just give the place a new look! Alex had just hung a new dartboard on the wall and was stepping back to admire his handiwork. Ian and Jamie actually weren't too sure, and Davey hardly looked up from where he sat at the bar. Well it's kind of diff'rent, now, isn't it? allowed Jamie. Yeh, it looks simple - no doubles or triples or anything agreed Ian. And just multiples of 5, added Davey, who became curious enough to walk over. There's a lot of scores no one could make on that board ... so, what's the point? That's exactly the point, beamed Alex. Simplicity! Usually you blokes don't like my propositions, cuz they're a little bit beyond yer brains don't ya know. So I'm making this one really easy to understand. Ian started twitching, and Jamie shuffled his feet a bit. They'd heard pitches from Alex before, and hearing that this one was simple made them a bit edgy. I'm thinking of a number, continued Alex, an easy one: 25. You get two darts and all you have to do is score 25 points. Look at the combinations that win for you. Even odds, and I'll even take away the out of bounds. If you don't hit a number, you throw another dart. Two darts that score, and the score has to be 25. Who's ready for a challenge? When the boys were silent, Alex stepped up the pitch. All right, two to one odds your quid against my two. Like taking candy from a baby, but you caught me in a good mood tonight. Ian shook his head, Jamie sat down to think it over, and Davey sauntered back to the bar. After a moment, Davey hollered, make it 3 to 1 and you're on. Ouch! cried Alex, if I weren't such a sport I might not agree, but hey - we're friends, aren't we? Let's see what ya got! Assuming that Davey was no great shakes at aiming the darts, with the only thing assured being that two darts end up scoring points, did Davey make a good bet? Or did Alex do his friends in, one more time? The radii of the four circles are as shown: 1, 2, 3 and 4 in some units.

Think what it means to survive. It's more than just getting past the first encounter. What happens when an indefinite amount of time has gone by?

It's independent of the number of false suggestions.

I'll play the game ... What's the difference between a duck?

Ha! One of the benefits of being retired.

There's an old parlor trick where one person tosses some old magazines on the floor in a Tic-Tac-toe arrangement like this. +-----+-----+-----+ | | | | | A | B | C | | | | | +-----+-----+-----+ | | | | | D | E | F | | | | | +-----+-----+-----+ | | | | | G | H | I | | | | | +-----+-----+-----+[/code] Another person [an accomplice] is then asked to leave the room, while the others choose one of the magazines. Say it's magazine F. The accomplice is then summoned back into the room. The first person takes a yard stick and points to magazine G and asks [color=#8B0000]Is it this one?[/color] The accomplice answers No. He then points to say magazine B and asks [color=#8B0000]Is it this one?[/color] The accomplice answers No. Several others, say H, A and E are suggested, and the accomplice in each case answers No. Finally he points to magazine F and asks [color=#8B0000]Is it this one?[/color] The accomplice answers Yes. How is this done? There is a variation of this trick: when the chosen magazine is suggested, the person asks [color=#8B0000]Is it this one?[/color] in a high-pitched tone of voice. Immediately someone thinks they've solved it and volunteers to leave the room while another magazine is chosen. But this time, a high voice is used when suggesting the wrong magazine, and the wrong answer is given. Other phony "tells" can be used for the chosen magazine, such as pausing, or emphasizing: [color=#8B0000]Is it .... THIS one?[/color] One by one someone thinks they've solved the puzzle. But in each case they can be shown to be wrong. Only the accomplice knows the trick. What is it? Hint: The chosen magazine can be the first one that is suggested. There doesn't have to be a wrong suggestion that precedes the correct one.

Kudos, however, to octopuppy for the best answer IMHO. He made it immediately obvious. naveed is a close 2nd. Again, IMHO.

These all look good except for 18 12 M in a Y - 12 meters in a yard Nice going.

Bumping this since some parts are not answered. <_<

Corollary: There are two types of people in the world: those that divide people into two types and those who don't.

Unless the letters can be used more than once, there are no 5-letter words there. If repeats are allowed, I think these are the only 5+ letter words available: Kimono, Knoll, Million, Minion, Onion I await the answers.

You got it. How was your skiing?

It's a wonderful result, really. The answer is the same for any radius. Except the radius must be at least 3" -- so that a 6" hole can be made. Read through the thread to get more information.

I first read this paradox in Martin Gardner's "The unexpected hanging ..." A prisoner was sentenced by a judge to hang, the following week, on a day he could not predict. His lawyer reasoned like the brilliant student here, and he convinced the prisoner he was safe from execution. On Wednesday, however, the hangman executed him. Much to his surprise. To analyze, consider the judge saying simply, "you will be executed next week on an unannounced day." Now the prisoner fears for his life each day. Adding the constraint "you can't figure out which day" really adds nothing to the situation. It means only that the Judge makes the decision independently. We can make it simpler. The judge says "You will be executed within one day. You can't know what day that will be." The lawyer says, well, if it's within one day it must be tomorrow. Since we know it must be tomorrow, it can't be tomorrow. The prisoner is executed tomorrow - unexpectedly. The reasoning of safety is unreliable: certainty that it won't happen makes the happening unexpected and therefore permissible. The operative statement is "you will be executed within one day." The rest is a red herring.

I'm late to the game on this ... sorry. Interestingly, if the ones with dirty faces don't reason correctly, all the monks who do reason correctly - including the 45 clean ones - get off to wash at the following stop!

[1] Do the Monks know [or do only we know] that only five of them have soot? [2] Do the Monks know that at least one of them has soot?