Nuntar
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OK, I've set quite a few puzzle recently so this one will be just a quickie to pass the torch to someone else. No rank points.

1, 2, 6, 20, 70, ?

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lopsidation
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Now, ordinarily I'd say that if the first two terms are a and b, the third term is ceil(b^2/a)+2, so the next term is ceil(70^2/20)+2 = 35*7+2 = 247.
But you said this was a quickie so I'm definitely missing the obvious solution.

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stigant
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Your formula would make the 5th term 69, not 70.

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Nuntar
Level: Smitemaster

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1, 2, 6, 20, 70, 252, ?

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lopsidation
Level: Master Delver

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It's the numbers down the middle of Pascal's triangle! ..., 924, 3432, 12870, ... comes next.

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Nuntar
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You got it!

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50th Skywatcher

lopsidation
Level: Master Delver

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Okay, this one should be pretty easy:

This morning, Halph was waiting to unwrap his Christmas gifts from Beethro. His mom, Vonifa Budkin, had said that everyone had to wait until 8:30 to start the annual gift raid. Being both impatient and a puzzle fanatic, Halph noticed that he could form an equation with the time on the clock: 8:26 -> 8-2=6. He decided to call times like these good times, and times when you couldn't make an equation bad times. (He decided that you can only use +, -, /, and *, and no concantenation, so 10:25 -> 10=2*5 isn't allowed.)

Halph gave himself a puzzle: Are there any bad times that rearrange to make good times? He had almost solved it, but *click* the clock changed to 8:30, and off he went to unwrap his new Kids' Safe Smiting Sword (TM).

Well? Are there any bad times that rearrange to good times?

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Nuntar
Level: Smitemaster

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19:23 -> 19:32

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lopsidation
Level: Master Delver

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Sorry, forgot to mention: it's a 12-hour clock. No second hand either. Nice try though.

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Nuntar
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Then it's not possible, but it's very difficult to formulate a watertight proof. If the time is three digits then it's easy to see that if you can make an equation, you can do so in any permutation:

a = b + c
a = c + b
b = a - c
b + c = a
c + b = a
c = a - b

But I can't see how to conclusively prove that you can't do it for four-digit times without listing cases. Especially as it has to depend on the fact that the second digit is at most 2 and the third digit at most 5; if either of these were relaxed there would be a solution.

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lopsidation
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It certainly is possible. And yes, it has to be a four-digit time.

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Maurog
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11:45 -> 11:54?

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lopsidation
Level: Master Delver

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1*1+4=5

1*1=5-4

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TripleM
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Well, I don't have a puzzle, but:

Nuntar
Level: Smitemaster

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Ah!

10:13 -> 11:03

There are seven solutions, as TripleM said, because the units digits can be anything higher than 2.

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50th Skywatcher

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[Last edited by Nuntar at 12-27-2008 12:44 AM]

lopsidation
Level: Master Delver

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Wow! You've done it!

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

lopsidation
Level: Master Delver

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Nuntar? You there?

New rule suggestion: If it's been more than a week and the next person hasn't responded yet, anybody can put up the next puzzle.

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Kwakstur
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[Finishes reading all 70-something pages]
[sees prompt to post question]
[thinks of something rediculous]
Alright, then...

So, 1024 prisoners are given a mix of red and white caps and told only the color of their own hat. They can communicate with eachother, but they'll get killed in the process. 1023 die. The last prisoner has to climb up a pair of 50-foot long ropes and maximize the distance he falls.
The rest (about 0) are stranded on an island with a Charizard and 11 poisoned wells mixed with water. They are driven by bus to well 11, while the Charizard takes water from the ocean. The pair exchange water. All the prisoners die. The water is super effective on Charizard! Charizard fainted. *roooaaar*

What color is my hair?


By the way, you can tell from doing something to those paragraphs. COMMENCE! AFTER THEM, MY PRETTIES!


Edit: It's not that hard, people. Especially not if you've ever tried to do notpr0n.

...wow... It's hard to believe that at some point Mattcrampy couldn't get a puzzle to last more than an hour in this thread.

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Also known as ExpHP everywhere else.

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[Last edited by Kwakstur at 01-20-2009 08:52 PM]

lopsidation
Level: Master Delver

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Italicized letters: d w n l a m k b o r p n w b h r o x s
Which isn't a caesar cipher. Therefore I am stuck.
The italics had better not be a red herring...

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Tim
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Kwakstur wrote:
What color is my hair?

That's pretty easy. According to the Member Pic Thread, you must be

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Kwakstur
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Okay, I'm pretty much going to give it away now...

Let me elaborate on a comparison I made earlier. In not pr0n, a lot of its puzzles require you to input both a username and a password from clues derived from examining the page, its url, and its source code.


What about when, among all the red herrings, you can only find one working lead, and you can't unambiguously get two words from it?

Messing around with HTML source can sometimes make you overlook a logical division.

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Also known as ExpHP everywhere else.

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[Last edited by Kwakstur at 01-20-2009 08:54 PM]

lopsidation
Level: Master Delver

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[thinks of something rediculous]

HA! Rediculous = Red!
Seriously though, I have no idea. I was terrible at notpr0n...
and there's no way you could change the page source, right?

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"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Nuntar
Level: Smitemaster

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I've checked the page source, and there is nothing unusual at all in the lines corresponding to the original post -- just the words exactly as you see them except for <i> tags around the italicised letters.

I dunno, perhaps the answer is "brown" because the html tag for a line break is <br>, which could also be an abbreviation of brown?

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50th Skywatcher

Kwakstur
Level: Smiter

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You don't need to look at the source for this. HTML is disabled anyways on caravel, so it's not like I could exactly hide stuff in it. Watch this.

Click <a href=forum.caravelgames.com>here</a> for no response.
<!--camo shirt: haha u cant c me-->

Nuntar wrote: I dunno, perhaps the answer is "brown" because the html tag for a line break is <br>, which could also be an abbreviation of brown?

Correct and incorrect. Yes, it's brown. No, that's not why.

What I was saying about messing arround with HTML was, once again, specific to the not_pr0n comparison. Level 9 spoilers:
My text, like that, was divided by paragraphs; it had the logical division of a line break. But you didn't need to look at the HTML source. You might have looked at and messed around with the BBCode source (BBCode is the stuff like [b]), which could've made you delete and therefore forget about the line break, hence my hint in my second post.

Either way, here's the letters for each paragraph:

dwnlamkbor
pnwbhroxs

Now the puzzle gets a bit evil. You could figure out what to do with these two sets of letters after enough trial and error, but examining the text itself provides clues to what to do (unfortunately, these clues are, in typical fasion, completely inconspicuous). I used the word "mixed" in both paragraphs. These paragraphs are also kind of a bunch of stuff mixed in with eachother.
In hindsight, I really should've also planted the word "share" into both paragraphs, too. Instead, I planted the word "pair," referring to pairs of letters. Not quite as helpful, nor even as noticeable.

Anyways, so the letters from a color are mixed in. And they're shared by the two paragraphs. What letters are those, then?

b r o w n

You might find one of these necessary right about now.

____________________________
Also known as ExpHP everywhere else.

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[Last edited by Kwakstur at 01-23-2009 05:13 AM]

stigant
Level: Smitemaster

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Here's the problem with this puzzle. I almost guessed "dark brown" after looking at the letters, but couldn't see what to do with the leftover letters. I didn't need the all the subtle clues (paragraph breaks, "Mixed" etc) to see that, but I couldn't justify the solution without finding something like those clues. But your subtle clues don't really do a very good job of resolving the issue. There's nothing in your solution that suggests that there are extra letters. "Mixed" doesn't really suggest that. And the paragraph break doesn't really help either in this case because there's no real need to break the solution into two parts.

In general, I hate puzzles like this. That's just my opinion, and I know that plenty of people get lots of kicks out of them. But to me they always, even after I have the solution in front of me, seem too random to be entertaining. They're about one step up from the "Find the next number in the sequence" puzzles. It's too easy for reasonable people to arrive at completely different answers. For me, part of the fun of solving puzzles is that two reasonable people will always arrive at the same solution no matter how they get there. That connection never ceases to amaze me.

I'm not calling for a change to the rules for this thread, I don't mind if these not-pron-type puzzles get posted here. I'm just trying to explain why I think this particular one ended up falling flat.

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lopsidation
Level: Master Delver

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Yeah, that was a nice puzzle, but it was a bit unfair- especially since the formatting made it look like the puzzle was only one paragraph.



____________________________
"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."

Nuntar
Level: Smitemaster

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In a long ago and far away land, there were two neighbouring kings, the kindly King Erik and the cruel King Bill. King Erik loathed his neighbour, but for the sake of peaceful relations between their two kingdoms he had to put up with his state visits.

They always took the same pattern. King Bill would saunter around Erik's palace as though he owned the place, then beckon to Erik to accompany him to a private room, sit him down, and say:

"My wives are prettier than your wives."

"That's because I chose women who are willing to marry me rather than buying up my nobles' surplus daughters."

"My wives produce more sons than your wives."

"I don't care; I love all my children equally."

"My wives are better at hockey than your wives."

"That's because it's such a violent game. My wives are better at keeping the palace life peaceful and harmonious."

It went on in this vein. Everything King Bill meant as an unforgivable insult, King Erik found a way of turning into a compliment. Until at last, King Bill could stand it no longer, and thumping his fist on the table, he roared:

"My wives are more intelligent than your wives!"

That, of course, was an incontrovertible insult, and required satisfaction. So all the wives -- each king had precisely one hundred -- were assembled in an arena for the great Intelligence Duel. The kings signed the following terms: each one would pose a problem to be solved by the wives of the other, and each wife who failed to solve the problem would lose her head.

King Erik went first, and posed the following problem. You'll have to forgive him; it was original when he thought of it.

"I will ask you all to stand in a line, all facing the same way, and I will put either a black or a white hat on each of you. I will ask each of you the colour of your hat, and anyone who gets it wrong will be executed. You are allowed to confer beforehand to decide on a strategy."

King Bill, like many boasters, was a complete liar, and all his wives were utterly unintelligent, apart from the youngest, Princess Celine, and she was too timid to speak up. So it looked like he would soon be losing half of his one hundred wives. But what King Erik didn't know was that King Bill, being cruel enough to tax his subjects to the hilt so that he could live in luxury, had a palace with all modern conveniences -- including time travel and Internet access. (Yes, this was before the hat puzzle but after the Internet. Must be a stray country from The Princess Bride.) So of course while they were conferring, one of them zipped forward to after the Caravel Forum was invented, read the Puzzle Tag thread, and discovered a strategy that allowed all but one of them to survive. So naturally, they arranged for Princess Celine to be the one who had to die, because she was only thirteen years old and too timid to stick up for herself.

(The other wives were too stupid to realise that Princess Celine could have made sure all the rest of them died by reversing the answer she was meant to give. But as she had only been married to King Bill for a few days, the bullying ways of his court had not yet rubbed off on her.)

So, Princess Celine was condemned to death, and came up to the dais where the two kings were seated for her sentence to be carried out. She gave one last look at her husband and smiled as though to say she was glad to be free of him, and then glanced at King Erik, and suddenly realised that not all men were cruel and cunning, and that some were handsome and pleasant and caring, and tears came into her eyes, but it was all useless. And King Erik looked down on her and saw how beautiful and fragile she was, but the word of a king is his bond, so with heavy heart he lifted up his sword to strike the fatal blow.

Then King Bill, seeing what was going on, thought he would like to play with these two a bit further for his own amusement. (Besides, it saved him having to think of an original puzzle.)

"Dear friend," he said, "I can see you would like to possess that girl. Now, I can release you from your sworn promise, but I will only do so on one condition."

"What's that?"

"Why, that you let me use as my puzzle the same puzzle you set my wives. Only, you will change the conditions for me too, namely that any of your wives who name an incorrect colour will be given to me rather than executed."

King Erik frowned, for he knew all his wives would look on being married to King Bill as a fate worse than death, but then he looked at Princess Celine again and realised he would happily part with all one hundred of them to get to spend an hour in her company, even if it had meant both of them had to die immediately afterwards. So when it came to losing just one wife -- for he was sure that if King Bill's wives could solve the puzzle then his could -- and getting to spend the rest of his life with her, he had no hesitation.

"There's just one catch," King Bill said with a wicked grin. "You see, unlike you, I can afford the most up-to-date range of dyes. My hats come in six colours, not just two."

King Erik stood there for a moment, stunned. Assuming -- since his wives have all lived with him long enough to learn kindliness and compassion -- all of them want as few as possible to be given to King Bill, what is the largest number of themselves they can save?

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50th Skywatcher

stigant
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I'm pretty sure you can save all but 1 wife with any number of colors. Assign each color a number from 0 to n-1 (n = number of colors). For example, with 6 colors, let
Red = 0
Orange = 1
Yellow = 2
Green = 3
Blue = 4
Purple = 5
The person at the back should add up all the numbers in front of her, divide by n (in this case 6) and keep the remainder. Then guess the corresponding color. All subsequent wives will know the colors of all wives between the first wife and them, the colors of all the wives in front of them, and the total (mod n) of all the wives together, so they will be able to determine their color by adding up all known hats (mod 6), and then subtracting from the total of all hats (again mod 6).

This is essentially what happened with the black/white hat line but using 2 instead of 6 and "odd" and "even" instead of 0 or 1. For example, using a shorter, 6 person line for brevity, suppose the last 5 people have the following hats:

? R B G O G

The first wife will add up the hats (0 + 4 + 3 + 1 + 3 = 11), divide by 6 (11 / 6 = 1 r 5), keep the remainder (5) and guess that color (Purple).

The next wife will add up the hats in front of her and those between her and wife #1 (ie 0) (4 + 3 + 1 + 3 = 11) divide by 6 (1 r 5) and then subtract from the total (5 - 5 = 0 = Red).

Wife 3 adds up the hats in front of her (3 + 1 + 3 = 7) and between wife 1 and her (0), mod by 6 (7 / 6 = 1 r 1), subtract from total (5 - 1 = 4 = Blue).

Wife 4 adds up the hats in front of her (1 + 3 = 4), between her and wife 1 (0 + 4 = 4) for a total of 8 = 2 mod 6. Subtract from total 5 - 2 = 3 mod 6 = Green

Wife 5 adds up the hats in front of her (3) between her and wife 1 (0 + 4 + 3 = 1 mod 6) for a total of 4, then subtract from 5: 5-4 = 1 = Orange.

Wife 6 adds up the hats in front of her (0) between her and wife 1 (0 + 4 + 3 + 1 = 2 mod 6), then subtract from 5: 5-2 = 3 = Green.

Wife 1 is of course doomed, but all other wives guess correctly.

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[Last edited by stigant at 01-25-2009 12:04 AM]

Nuntar
Level: Smitemaster

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I can't find any fault with that solution. Well done!

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50th Skywatcher

lopsidation
Level: Master Delver

Rank Points: 176
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Poor Celine. If only she had been less timid, she could have spoken up with her method, which spared everyone a certain death and took advantage of King Bill's greediness:

Wife #1 picks entirely randomly,
then Wife #2 looks at the 98 people in front of her and uses the original Puzzle Tag strategy, switching the result if Wife #1 said "black".

Using this method, the two wives in the back can do no better than a 1/2 chance of death, even if they get greedy and decide to stray from the plan.

____________________________
"Happiness is like a cat. If you pay no attention to it and go about your business, you'll find it rubbing against your legs and jumping into your lap."