bonanova

Amazingly, that's not the answer. Why?

Right. Sort of. You answered the question: what are the values of p and q for which a minimal number of steps are needed ... etc. The answer needs to be true for any values of p and q.

Consider two solids: a unit-length tetrahedron [triangular base pyramid] and a unit-length square pyramid. The visible sides of these solids, if the single square face is placed on the table, are equilateral unit-length triangles. Glue a face of the tetrahedron to a face of the pyramid so that the points of the two triangles exactly coincide. How many faces does the new solid have?

You just bought a rectangular bar of chocolate. It has been marked into pxq tiny squares. Since you are of generous nature, you want to share it with me. So you wish to break the bar into its individual constituent squares. At each step, you may pick up one piece and break it along any of its marked horizontal or vertical lines. What is the smallest number of steps that will accomplish this?

What is the solution for 2k - 1 prisoners? [k is ingeter >2] What is the general solution for n>3 prisoners?

Folks, We're all ages here at Brainden. I'd prefer we assume that none of the riddles posted here have answers that need asterisks ;-) Thanks, - bn

I was amazed by this story. You have it. As I understand the story, the 3rd base coach held up the runner from 2nd base, who apparently didn't hear in Infield Fly called and thought he had to advance. But the runner from 1st base didn't see the coach's signal and continued running, thereby passing the first runner. In the ensuing confusion, the ball, still in the air, was forgotten. Until it came down and hit the surviving runner. Only in baseball can things like this happen. I've heard only one baseball story that tops this one, and I'll post it separately in a non-puzzle forum.

Most often this riddle is shown as unsolved. K was one of the attempts - see esp the 1st stanza. Even the acknowledged answer is a stretch for some of the clues

Not sure how to apply this yet to the whole thing, but I might be gone until Monday, so hopefully this helps someone. You have the optimal strategy for 3 players. Note that 3 is 1 less than a power of 2, and for such cases, the odds become very favorable. Now, can you generalize it to 7 or 15 prisoners?

At least Honorable Mention that that one ...

That's it. Nice going.

Thanks gmarsha11, Three points: [1] Your scenario satisfies no assists, no ground, no leather. Nice job. But ... [2] I clarified in post #4 that the defensive team made no plays on the ball. In your scenario, the defensive team makes a play. [3] Showalter's triple play happened either in spring training [i think] or else in the minors, so it's not in any book; nevertheless it was scored according to normal baseball rules. The "riddle" is to find a triple-play scenario where the defensive team does not make a play and the ball doesn't hit the ground. It doesn't have to be the play he described: remember the OP asks: how could this have happened?

Further research reveals it's been done approximately 50 times. Although prior to 1956 it had happened only 5 times, owing to the absence of the split-fingered fastball in the previous era. And [i believe] only one pitcher has done it more than once - in MLB.

Interesting scenarios all, but none fits the conditions, yet.

My source says one of those you mentioned did it more than once. But, Google doesn't lie: I'll accept the answer.

How much do you pay? Satisfied with the phone service? In BS's triple play, the entire defensive team could have left the field after the pitch was made. The defensive team literally was not involved in the outs: no tags were made. So let's say the pitched ball did not touch ground, leather, or skin. It's possible/probable [don't know all the applicable rules] some put outs were ascribed to certain players.

Great guesses.

Yup. I have the same text you posted. Maybe from the same website. I think it's the only website that has it. The other sites just show the riddle unanswered.

I sit stern on the rock while I'm raising the wind, But the storm once abated I'm gentle and kind. Kings sit at my feet who await but my nod To kneel in the dust on the ground I have trod. Though seen to the world, I am known to but few, The Gentile detests me, I'm pork to the Jew. I never have passed but one night in the dark And that was with Noah alone in the Ark. My weight is three pounds, my length is a mile, And when once discovered, you'll say with a smile, That my first and my last are the pride of the isle.

Bucky Showalter tells of a triple play where the ball never hit the ground or touched leather. Because of this, it was a special kind of triple play: no assists were recorded. How could this happen?

What is the record for most strikeouts recorded by a pitcher in one inning? Who has achieved it the most times?

Fair coin toss means a coin is tossed for each prisoner. If it's heads [say] he gets a black hat. If it's tails he gets a white hat. One can conclude that there is no guarantee of equal numbers. The prisoners are taken aside and asked to guess [or pass.] No communication is permitted. One can conclude that prisoners do not know the response given by other prisoners. Each prisoner answers only once. [implied but explicit in OP] Net: each prisoner's strategy is guided only by what he sees. I've added this starter suggestion to the OP: Starter suggestion - suppose there are only 3 prisoners. Work out strategies that might improve on the 50% that seems intuitive. Then try out your strategy for 16 prisoners, where survival could be quite likely.

Usually you add s to make singular plural. My last puzzle added s and made plural singular. Now add c to make singular plural.

Warden Smith has been transferred to yet another prison, and pity his new set of prisoners! This time he announces that: tomorrow ... they will be taken to the courtyard and arranged in a circle. each prisoner will be given a white or black hat as determined by a fair-coin toss. each prisoner will be able to see the hats on all the other prisoners. no prisoner will be able to see his own hat. no communication will be permitted. Then, unless at least one prisoner guesses, and every prisoner who does guess guesses correctly, all the prisoners will be executed. That is, if they all pass, or if anyone guesses incorrectly, they're all dead. That makes the prisoners desperate enough to call you in as a consultant. You meet with them the night before the event, to advise them what to do. One prisoner suggests that they will have an even chance of survival if one person guesses, and all the others pass. What do you advise? Edit - added 4:50 pm EDT 30 May 2008 Starter suggestion - suppose there are only 3 prisoners. Work out strategies that might improve on the 50% that seems intuitive. Then try out your strategy for 16 15 prisoners, where survival could be quite likely.