Arctic's Riddle Challenge! - 5 Cards, A magic trick, and the mysterious guesser.

[bury the year]

Wait. I need to clarify. Is there a specific number of pink and blue hats?

[Ăɍȼẗîȼ]

It's not known.

[bury the year]

[spoiler=Answer.]

100 wizards can be saved, and 1 has a 50% survival rate.

[spoiler=Why?]

During the night of planning, the wizards work out a code for the declaration of the wizard in the back, number 101. Before he makes his announcement, he confirms with the others that if he says "pink," the quantity of pink-hatted wizards and cyan-hatted wizards are both even, and if he says "cyan," both quantities are odd. This code will also be used by the others.

 

Now, let's say wizard 101 looks in front, at all other 100 wizards, and there are an even number pink wizards and cyan wizards. Therefore, he announces "pink," regardless of what he thinks his hat is. He was wrong, and he is burned to death.

 

The next wizard, wizard 100, therefore knows that there were an even number of pink and cyan hats from the view of #101, which includes wizard 100, or himself. He then looks at the hats in front of him, and compares it to the answer which the wizard behind him gave. Since #101 said "pink," there are even quantities. Now, since #100 can see an odd number of cyan, but an even number of pink, he can deduce that he is the last pink-hatted wizard, and says "pink." He is correct, and is freed.

 

Number 99 is next, and he uses the declarations of wizards 100 and 101 to figure out his hat color, and gives the answer to the ones in front. Continue ad infinitum.

 

 

[Guest Welche]

If they can have codes then life is easy.

 

Code is made for number of cyan hats. If even say pink, if odd say cyan. Everybody keeps track, nobody dies.

[Ăɍȼẗîȼ]

Congratulations to Deja Cru.

[Guest Welche]

You place the cards numerically. That is so easy.

[Ăɍȼẗîȼ]

How? Please be more specific

 

Assume the worst case, again.

[Guest Welche]

Ok, so when I am organizing the deck I put the cards ace, 2,3,4,5,6,7,8,9,19, jack, queen, king.

[Ăɍȼẗîȼ]

5 Cards are given only. and Bob chooses the 5 cards, and my friend is out of the room when this happens.

[Dark Mousy]

Hmm... This is interesting, but why 5 cards?

[Guest Welche]

The entire deck was organized numerically and the five cards then must have the middle one be gone.

[Jericho]

All the cards in the deck are the same. One would simply buy 52 decks and make 52 decks of single cards (i.e. a deck of all Aces, a deck of all 2s, a deck of all Kings, ect.).

[Ăɍȼẗîȼ]

@ Jericho : Assume a standard 52 card deck.

 

@ Welche: You don't pick the 5 cards, some one else does so arbitrarily.

[Ăɍȼẗîȼ]

Rules-> Read before you post:

1) Don't post anything that is unnecessary' date=' or stupid.

2) Do not assume anything that shouldn't be assumed. I.e. Can the wizard's escape during the night? They could, but we don't know that.

 

3) You are only allowed to use premises on the question.

4) Solve this problem TOGETHER, as a whole of YCM.

5) If anyone wants to donate, then they are welcome to, any donations would go into prizes other than possible reps.

 

[hr']

 

Say me and my friend are going to play a magic trick on someone called Bob. (There is some system arranged before hand between me and my friend.)

 

Okay my friend leaves the room.

 

BOB chooses 5 cards. (assuming a STANDARD 52 card deck.)

 

I CHOOSE a card to hide from the 5 cards, and I CHOOSE the order of the remaining cards to place on the table.

 

My friend comes in, and he looks at the 5 cards on the table, and he is able to tell exactly the card that I hid. (note he hasn't seen the 5 original cards)

 

Bob is absolutely stunned.

 

What was the system arranged before hand?

 

Assume the worst case when Bob chooses cards.

 

---

[spoiler=Past Problem #1]

Say there are 101 wizards, sentenced to the Death by the King Wizard.

 

The King Wizards says to the wizards:

 

"I am a good King. Tomorrow, I will line you all up in a single file straight line, and remove your wands so you can't use magic. I will place a hat on each wizard, it is either Pink, or Cyan. You must guess the color of your hat! If you get it right, then you live, if you should get it wrong, you'll BURN!!!"

 

"Of course, to be fair, the wizard at the end of the line gets to see all of the hats in front of him..., but in exchange for that, he must go first! You will have tonight, to say your last words... (You are not allowed to say anything but guess the color of your hat.)"

 

Of course, none of the wizards wanted to die. So they talked, and brainstormed all night long. They came up with a plan.

 

What plan will save the most wizards in the worst case?

 

For example:

First wizard says the second wizard's hat color instead of guessing their own. The second wizard says whatever the 1st wizard says. In the worst case, this saves 50 wizards.

 

Congrats to Deja Cru!

 

 

 

See bolded. Also, see:

 

last edited Yesterday 05:52 AM by Ăɍȼẗîȼ.

 

Now shut up.