Potpourri Puzzling for Paralysis - Not Adequate For Real Lif

[Aarondalf]

I am back

[Dragon Phoenix]

Too late again - congrats

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Luna sees me as flying orange-brown and orange-yellow, dark but with stars in the background...

[Pefrection]

THe original url for the greylabyrinth was www.wx3.com/~greylabyrinth, (maybe without the tilda...)

[Pefrection]

Five basics "tastes"
sweet
sour
salty
bitter
umami

[NewHere]

Was the wx3.com addy before the mediaone.net addy? Just asking: I'm new here, so the question seems a little unfair;-}

[Nit Pick]

I'm just wondering: shouldn't the puzzle title be 'Puzzling AGAINST Paralysis'? The way it reads now seems like its pro-paralysis.

[hank]

I find the first puzzle intriguing. Although I can't provide firm proof, I suggest that it is always possible to cut a ham and cheese sandwich in half. jBased on the fact that it takes 3 independant equations to get a unique solution for three variables, I suggest that there are three separate parameters to define a cut through three separate materials, mainly ham,cheese, and toast. this could not be done if we include butter. The variables are the location of the initial cut, the horizontal angle of the cut, and the vertical angle of the cut.

[hank]

9, There are a minimum of 13,281 coins . I think that solution maybe unique. What do you think?

[hank]

3. We dealt with this puzzle over a year ago. Certainly mithrandir should remember.I can't seem to locate this discussion however, so it may have been deleted.

[tv snake]

I leave the country and Aarondalf gets the 100th puzzle...

I get the 2000th post though!!

[Courk]

I found this when searching for Grey labyrinth on www.searchalot.com

quote:

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THE GREY LABYRINTH
I created the Grey Labyrinth as a playground for curious...
http:/www.wx3.com/labyrinth/biblio.htm

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[Courk]

http://www.wx3.com/labyrinth <--- thaaaaaat's it! I contributed! YES! Woooohoooo!

Sorry, It's my first...and last...:-/

[tv snake]

In the absence of any previous discussion...

3. When the rubber band is stretched it pulls the ant along with it. So the ant can reach the end.

[OcularGold]

[Aarondalf]

Hmmm, there be a trick in it says I.....

[NewHere]

13281 coins in the chest, minus one for Jim, divided by five and times four is 10624. The second pirate to awake takes that sum and gives one to Jim, dives by five and gets 2124.6 coins in each pile. Sorry Hank.

[NewHere]

I think Jim and his pirate friends might be infinitely rich.

[Ghost Post]

#5 - I think these are the newly unfolded solar panels of the International Space Station (ISS).

[NewHere]

If the fifth pirate to wake has hidden an amount equal to one fourth the final contents of the chest, the chest must contain a number divisible by four, as well as the given five. The chest contains an even-number of coins (evenly disible by twenty).
The fifth pirate's hidden share must be divisible by five if it is a quarter of the final contents. It must also be an odd number, for otherwise when you add Jim's share of one, the fifth pirate must have woken to a chest containing an odd number. I'd like to hear pirate number four explain how he has hidden a quarter of that.
I went up through the odd multiples of five, trying to multiply by five, divide by four, and add one five times each in sequence without hitting a fraction.
Turns out pirate five hid 255 coins, 1020 were left in the chest at the end, and 3121 was in there to start with.

[Courk]

Work backwards.

1x4=4+1=5
5x4=20+1=21
21x4=84+1=85
etc. I don't have the time right now.It won't give the lowest # I don't think, but you know it hasta be less... Yeah, i was no help...ah well

[mathgrant]

I'm working on the coins.

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[This message is being edited by mathgrant (being edited right now).]

[Ghost Post]

Answer for the coins is 3121.

I'm working on an explanation.

[mathgrant]

I figured out it's 3121, but I wasn't the first, as you can see.

Explain:

The pirates start out with x coins.
One pirate takes out (x-1)/5+1--1 for Jim and (x-1)/5 for himself. Let's say a remains.

The next pirate takes out (a-1)/5+1--1 for Jim and the rest for himself. Let's say b remains.

The next one takes out (b-1)/5+1--1 for Jim and the rest for himself. Let's say c remains.

The fourth pirate takes out (c-1)/5+1--1 for Jim and the rest for himself. After that operation d remains.

The final pirate takes out (d-1)/5+1--1 for Jim and the rest for himself. e remains.

When the pirates wake up to find e left, the find that it divides perfectly. So each pirate got f more.

We have 6 equations:
1. x-1-(x-1)/5=a
2. a-1-(a-1)/5=b
3. b-1-(b-1)/5=c
4. c-1-(c-1)/5=d
5. d-1-(d-1)/5=e
6. e=5f

We substitute equation 6 into 5 and simplify to get

5. d=(25f+4)/4

Now we substitute that into 4 and simplify to get

4. c=(125f+36)/16

Substitute that into 3 and simplify for

3. b=(625f+244)/64

Plug this result in 2 and simplify:

2. a=(3125f+1476)/256

Finally substitute that into 1 and get

1. 1024x-8404=15625f

Now we need to use modulo arithmetic and a calculator. From 1 (and the fact that x and f are integers) :

15625f=-8404 (mod 1024)

I bet this is the first time in the GL where mod didn't mean moderator! Simplifying that:

265f=812 (mod 1024)

Eventually with help from a calculator we get

f=204 (mod 1024)

The minimum value of f is therefore 204. In that case 1024x-8404=3187500, 1024x=3195904, and therefore x=3121. This is clearly the minimum.

[This message has been edited by mathgrant (edited 12-05-2000).]

[mathgrant]

[parody of cheese]Ah, the power of mathematics.[/parody of cheese]

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[This message is being edited by mathgrant (being edited right now).]

[knightofni]

I did the coins prob. on my own and ended up w/ 3121 as well... looks like we have a winner (:

[knightofni]

And BTW, Image 1 of #6 is some of the text of the Voynich manuscript.

[dethwing]

i see my pirate post was worthless then. I got 3121 with paper pen and calculator.

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Potted plants dont anwser prayers
If you keep a stewed tomato in your shoe, it wont bring you eternal happiness

[NewHere]

Infinitely elastic rubber is not necessarily infinately stretchy...it just returns exactly to its original length when relaxed. The ant will reach the end when the super-elastic rubber reaches it's stretching limit (or soon after).

[Ghost Post]

Without going into hooks law and the like, in this context, elasticity refers to stretchability. Pulling the rubber band does not change anything given that the stretch is even. The ant will reach the otherend, taking exactly the same time it would have taken without any pulling. ie. 100 seconds.

[carebear]

on question 8, do you have to go over all of the edges, or just pass over all of the verticies?

[borschevsky]

Number 8 is vertices, not edges.

[wordcross]

On # 12 I just wanted to venture a guess and say Marco Polo, Since he did the whole China/India expedition before accurate maps. It's possible that he thought it shorter to go through Mongolia!

[knightofni]

Is number 5 a trick question? If it is, the obvious answer would be the sun...

[NewHere]

I thought about Marco Polo too, and found reference to him choosing to go through Mongolia instead of taking a boat to India, but I couldn't find reference to him actually arriving in India, instead going north into China. Also, there was no reference to him being in a hurry.

[Coyote]

The Minotaur can be pretty sneaky sometimes!

I believe the answer to #12 is Phileas Fogg.

[wordcross]

I agree with the whole "80 days" idea. He was in quite a hurry, and he did rescue that sacrificial woman in India...