bonanova

But I don't get the cold weather part.

Correct on both.

Supandi has it. Kudos. For the curious, spells at a distance are tempting, but that raises the question of receiving a spell unknowingly [before midnight at least]. So let's say that in all cases the giver and receiver of a spell both always know the spell has been cast. This is certainly the case if you were to cast a spell on yourself. As for acts of felony, like stealing another's wand, uh ... let's say that would force a delay and a do-over. As for female contestants, I neglected to mention the handsome Prince. My bad. Winning contestant gets to choose. Hey it's the nineties naughties. If you have other creative solutions, let us know.

In the Land of Midnight Spells, all magic spells have a built-in delay They do not take effect until midnight. Strange, you say, and with good reason. Depending on the time of day a spell is cast, the victim might have enough time to seek a remedy. Now, if the midnight delay is strange, the only remedy for a spell is even stranger. The only antidote for a spell is to receive another spell - before midnight mind you - because the two spells will then cancel. But only if the second spell is stronger than the first. As it happens in LMS, all spells are cast by waving a wand. The King of LMS knows all this, and it didn't take him long to figure out that his own survival can be guaranteed only if he possesses the Strongest Wand in the land. He can then neutralize an enemy spell by using his wand on himself:just before midnight. So the King proclaims a contest. Merlin, the King's Grand Wizard, and you, the King's Grand Logician, are given exactly one week to create the Strongest Wand in the land. At the end of the week you and Merlin will be summoned to the King's court. There, each of you will use your wand to cast the spell of death on the other, and then you will cast the spell of death on yourself. The contestant with the stronger wand will have neutralized the other's spell, but the contestant with the weaker wand will die at midnight. The surviving contestant will give his wand to the King and as a bonus he will receive the King's beautiful daughter to wed. You are worried. You know you don't have a clue about making wands, but Merlin does. He has made all the wands now in the Kingdom. He will have no difficulty making one more, that is stronger than all the others. So you rely on your skill as a logician. You devise a plan to make sure that Merlin will die and you will survive, and now you feel better. But, at the end of the week, Merlin realizes that you have no chance of making the Strongest Wand, and so you must have used your logic skills to devise another plan. After a moment's thought Merlin realizes what your plan must be, and he devises a counter plan to make sure he survives and you die. At the appointed time you and Merlin appear before the King. Each of you has a wand, and the spells are cast as planned. Sadly, at midnight you die, Merlin survives, and the King does not get what he wanted. What exactly happened here?

The procedure is not a construction of the minimal length condition. It's only a proof that when you eliminate a crossing you decrease the total length. The proof that an arbitrarily large number of pairs can be connected without crossings rests on the fact that whenever crossings are eliminated the total length goes down. To repeat the proof, Take all the possible pairings of the [artibrarily large] set of red and blue points. Each pairing has a certain total length. Select the pairing that has the shortest total length. This pairing has no crossing. Proof: if it had a crossing, its length could be shortened. OK?

The first question was posed on April 6 2008 and answered [p=1/4] here. The interpretation was that two points were chosen at random on the line segment and the cuts were made at the points. The coin toss problem sounds familiar but I didn't find it in search.

When you solve a puzzle, you take the statements as true. Otherwise you're solving something else. Under the statement of the problem, you can guarantee the lives of 19 prisoners.

DaGriller, This forum is not the place for trash talk. Even if you took the previous post as out of bounds, your post goes way beyond it. Take your pills <_< and PM me if you have a gripe about other posts.

Circles intersect at two points. Are you saying both intersections are at right angles, or can one intersection be something else?

Those numbers seem small. Compare with 3/4 of the individual areas.

Great job. How did you find it?

Prime asks for a solution that uses integers and rational numbers.

What if the wind speed was the same as the plane's air speed? Are you sure the headwind leg would take only a blink of an eye?

Where did you come up with the idea there were 10 red hats and 10 black hats? Construct a sequence of 5 red and 15 black hats and try the method. Tell us how it comes out.

As long as you simply offer opinions, Denizens can't critique you - they can only stand in awe of your brilliance. How long before you grace this forum with, for example, the "correct" winning probability for Prof T? Hint: If you don't want to disclose all your breakthrough thought processes, you could just give your opinion of the answer and let someone here prove that you are or are not right.

Go ahead and post it here. We'll confirm it or not.

There are a number of ways to make a statement then ask a question which presumably references the statement. I can't think of one, yet, that couldn't be incorporated into the question.

Hey, that's my quote!

The genre is your idea, which I think is an interesting one. I may do a few more if you don't mind.