[bonanova]

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?

[dms172]

I'd say the king really was trying to get the

grand magician killed because the GM was

the only one stronger than the king and

the only one who could over throw the king.

[Guest]

I deduct that

I know Merlin will show up with the strongest wand.

Prior to the spell off, I cast a death spell on myself with a regular wand and show up at the court with a stick (non functional wand). I theorise that Merlin's spell on me will then neutralise my earlier spell and his spell on himself will kill him, as my stick would not have cast a spell on him at all.

Merlin realises this and counters it by coming with a stick too. Thus only I am cursed (by myself) and die at midnight, while Merlin weds the princess in exchange for a useless stick that he would offer to the king as the greatest wand of all times.

Edited October 1, 2008 by Supandi

[Guest]

I deduct that

I know Merlin will show up with the strongest wand.

Prior to the spell off, I cast a death spell on myself with a regular wand and show up at the court with a stick (non functional wand). I theorise that Merlin's spell on me will then neutralise my earlier spell and his spell on himself will kill him, as my stick would not have cast a spell on him at all.

Merlin realises this and counters it by coming with a stick too. Thus only I am cursed (by myself) and die at midnight, while Merlin weds the princess in exchange for a useless stick that he would offer to the king as the greatest wand of all times.

I like it, except for the fact that the wizard outsmarts the logician. Maybe Merlin first casts the logic spell on himself?

Edited October 1, 2008 by Chuck Rampart

[Guest]

I deduct that

I know Merlin will show up with the strongest wand.

Prior to the spell off, I cast a death spell on myself with a regular wand and show up at the court with a stick (non functional wand). I theorise that Merlin's spell on me will then neutralise my earlier spell and his spell on himself will kill him, as my stick would not have cast a spell on him at all.

Merlin realises this and counters it by coming with a stick too. Thus only I am cursed (by myself) and die at midnight, while Merlin weds the princess in exchange for a useless stick that he would offer to the king as the greatest wand of all times.

This is pretty cool... Is this the real answer??? If not I like it

[Prime]

... and

you, the King's Grand Logician, are given exactly one week to create

... 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 preclude some female constituency of the Brain den from participating. Many of them do not want to marry king's beautiful daughter.

You could cast your death spell on yourself first wth your weaker wand and then wait until Merlin casts his both spells negating your pending doom, then cast your ineffective death spell on him.

But then Merlin could just use the weakest wand. But then you can just pick another stick from the bushes. Can a wand be weaker than 0?

The thing is, in the end, neither of you knows the other's choice of wand strength.

[Prime]

... 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.

There is an ambiguity in the statement of the riddle.

If contest goes as planned without any logical tricks and Merlin casts his spells first then both contestants would die. Your consequtive weaker spell cannot negate Merlin's strong spell on himself and on you.

Whereas Merlin's shooting first, suits you fine, if you pre-cast death spell on yurself, Merlin would cancel it, and your latter death spell on yourself could be canceld by you before midnight.

But Merlin is not entirely without logic skilsl himself. If he accepted the first shot, you know he has a logical counteraction up his sleeve, and you must in turn counter...

[Prime]

Perhaps, I misuderstood. The contestants first shoot at each other, then each at himself.

Still, some ambiguity remains:

1. Do you have to be within shooting range to cast a spell? That is can you cast at someone without them being aware?

2. Can you sense a not canceled death spell hanging over you? That is, do you know whether or not cancellation spell was effective?

[Guest]

You steal Merlin's wand and replace it with a bad one, but Merlin knew this, so he made an incredibly bad wand. You think you have a good wand, but you actually have a terrible wand. You cannot counter Merlin's spell, even though it was froma weak wand. Merlin counters yours, and te king is entirely without a decent wand.

There are many possibilities.

[unreality]

hey, this reminds me of a game I made yesterday

The King didn't get what he wanted because the two testees were too busy trying to figure out how to survive for sure rather than making the best wand. If the stakes had been less than death, more effort would go into making the best wand

So you know that Merlin can make a wand of any strength... certainly one better than yours. So you must use logic to survive, not necessarily with the best wand. And we know that eventually Merlin also used a mediocre wand (or a stick), since the King didn't get what he wanted

So what happened was you cast a spell on yourself with a NORMAL wand before going to the duel, and in the duel you brought a stick, or a magicless wand that looked like a wand, or whatever. Merlin's strong wand would counter your weak spell, then you would pretend to cast a spell on yourself, but you have a fake wand, so nothing happens. Which also means you didn't cast a spell on Merlin either, which means Merlin kills himself with his own wand

But Merlin has logic skills too apparently, and realizes that if he brings a fake wand too (and never casts a spell on himself at all, beforehand or not), then your original spell will kill yourself

However you, being the Logic Master, should've gone one step further than Merlin, and bring your mediocre wand to the duel (having cast the spell on yourself beforehand). Your attack will kill Merlin, since he has a blank wand, and then you can turn your wand on yourself to dispel your own

[bonanova]

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.

[Prime]

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 female contestants, I neglected to mention the handsome Prince. My bad. Winning contestant gets to choose.

If you have other creative solutions, let us know.

One must be a weak logician to fall for such a simple Merlin's trick.

Having upper hand in wand-making, Merlin can insure his own survival, but not your demise.

But first there are some assumptions to make to disambiguate the statement of the problem.

1. You know when spell is cust upon you, but can you sense the relative strength of the wand with which the spell was cast?

2. You always know of the spells cust upon you (by yourself, or others), but do you know of any spells hanging over your opponent?

I am going to go ahead and assume that no one (even Merlin) can tell the relative strength of wand without having it in their possession. And that no one knows of how many spells already hang over another person. Also, it is useful to assume that king knows a wand from plain stick and contestants will have to use some wand. No swithcing of wands in the middle of the contest.

Being a top wand maker, Merlin makes the weakest possible non-zero wand and shows up with it at the contest. After the contest and before midnight, he uses his strong wand to negate your death spell still hanging over him. Having figured that out, you cust additional spell upon yourself after the contest and also survive.

Merlin can ensure own survival with either weakest, or strongest wand at the contest. In first case, he casts additional spell after the contest, in the second -- he doesn't.

Without being able to sense relative wand strength, logician's survival becomes a matter of probability. Logician faces a decision of whether to cast an additional spell on himself after the contest. In either case, it is prudent for logician to precast a spell upon himself, when he is protected against Merlin's stronger wand.

The statement of the problem already tells us what happenned. Merlin survived, Logician died. Which means that Logician could not guess that Merlin had the weakest wand at the contest, and then made a misdjudgement with respect to the need of additional spell.

Trully mind buggling situation arises, when both survive and neither wants to marry kings daughter...

Edited October 1, 2008 by Prime

[Prime]

And to continue stumping dead logician into the ground, here is an infinite regress of reasoning to which I arrive:

It is always prudent to precast upon oneself before the contest.

Merlin can always ensure his survival, for he knows the relative strength of his wand compared to Logician's.

Merlin knows that logician's demise is effected by Logician's misjudgement on whether or not to cast cancellation spell upon himself after the tournament.

However, if Logician neglected to perform a pre-spell, then using strongest wand at the tournament ensures Logician's demise. (He would not be able to save himself with any cancellation spells thereafter.)

Knowing that, Merlin cannot pass this additional chance and must bring his strongest wand to the tournament, Logician knows to always perform a pre-spell.

Merlin knows that Logician expects him to bring strongest wand, and thereafter guess correctly to perform cancellation spell after the tournament and survive. Therefore, to con Logician into performing an extra deadly spell upon himself, Merling brings his weakest wand...

Logician knows, that Merlin knows...

[Prime]

...

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.

...

What I don't get is how Logician can even begin to think he made sure that Merlin dies? We agreed, he cannot cast any spells on Merlin without Merlin's knowing.

[unreality]

see post 10 of this topic

[Prime]

see post 10 of this topic

You show the resulting infinite regress in reasoning. However, you cut it off at one point alleging that somehow Logician will outcalculate Merlin. I am going to intercede on Merlin's behalf. Do not underestimate him! Just because he is a wand maker, it does not mean he has no logic.

The important point: Merlin can always ensure own survival. Not so for poor Logician, who seems to have only a 50/50 chance of guessing what to do after the duel.

But let me retract from some of my previous assumptions and make this problem definitively solvable.

I suggested that a simple non-wand stick (a zero-wand) should be prohibited. Now I take it back. They can use plain sticks and no one will know better.

Suddenly, Merlin's life is in danger. He does not know if the spell is hanging over him after the duel.

Let's make another reasonable assumption (already suggested by Unreality): survival is overriding motive, killing your opponent is the next priority, while keeping your good wand from king's hands, marrying his daughter/son not all that important.

Now Merlin must devise the way to ensure own survival. That in itself is a riddle so it goes inside the spoiler.

Merlin cannot afford not to know whether or not a spell is hanging over him.

The way he can solve that is to fasion a weakest possible wand and bring it to the contest.

Then if Logician used a plain stick, Merlin will end up cursing himself with a weak wand. If Logician used his wand, Merlin's weakest wand will fail to remove the curse.

Either way Merlin knows, the curse is hanging over him after the contest. Whereupon he can use his strong wand to remove it.

As this seems to be the only strategy for Merlin and Logician is capable to deduce it with ease, he knows what to do too.

Only in this way both survived, explained to King that their wands were of exact same maximum possible strength, married kings sons and daughters...

[unreality]

Yeah I know that it was an infinite regress, but I assumed that Logician > Merlin in decided "where" to stop in the infinite regress, just cuz the Logician is that good

[Guest]

I like it, except for the fact that the wizard outsmarts the logician. Maybe Merlin first casts the logic spell on himself?

I too thought it would be improbable but since the puzzle makes certain statements of fact like " Merlin realizes what your plan must be", "you die" and most importantly "the King does not get what he wanted" which reinforce the fact that the magician got lucky. While the logician should have thought of the magician's countermove, the puzzle conclusion indicates otherwise.

I went down the weak wand strong wand option but, while you would have privacy before a contest, you would not get any after it in the king's court for the sake of fair play and also as the King would not want a switcheroo of wands, which is really his main agenda. Hence any counter spell would not be possible post the contest. So the regression event would not arise.