Skylancer64
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These are all excellent solutions!

But you can do it with less than four planes.

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eytanz
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Oh, um, d'oh. I should have seen it, but I was trying too hard to be faithful to Red_Hawk's solution.

Follow my (= Red_Hawk's) solution up to step 6, repeated below

eytanz wrote:
1. Planes 1, 2, 3 start at the island.
2. Planes 1, 2, and 3 all fly 1/4H east.
3. Plane 3 gives 1/4T fuel to plane 1, and 1/4T to plane 2.
4. Plane 3 flies 1/4H west, reaches the island, and refuels. At the same time, Planes 1 and 2 fly another 1/4H east.
5. Plane 2 gives 1/4T fuel to plane 1.
6. Plane 2 flies 1/2H west, reaches the island, and refuels. At the same time, Plane 1 flies another 1/2H east.

(half-point recap - Plane 1 has 1/2 a tank left; it's halfway around the world (1H). Planes 2 and 3 are at the island, with full tanks.)

Now, here's how you do the rest without a fourth plane:

7. Planes 2,3 fly 1/4H west. Plane 1 flies 1/4H east.
8. Planes 3 transfers 1/4T of it's fuel to Plane 2
9. Plane 3 flies 1/4H east, and refuels. Planes 1 flies 1/4H east. Planes 2 fly 1/4 H west.
10. Plane 2 transfers 1/4 T of fuel to plane 1.

Note the situation now. Plane 3 is at the island with it's tank full. Plane 1 is at 1/2H west, with 1/4T fuel. Planes 2 is at 1/2H west, with 1/2T fuel.

11. Planes 1,2 fly 1/4H east, Plane 3 flies 1/4H west.
12. Plane 3 transfers 1/4T of fuel to plane 1.
13. All three planes fly 1/4H east, arriving safely at the island.

[Edited by eytanz on 01-27-2004 at 02:21 PM GMT]

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Skylancer64
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Perfect. Your turn.

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eytanz
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Okay, this shouldn't be too hard:

Suppose that you buy some numbers shaped like the ones on a simple digital calculator. You don't need to buy a complete set, because you can, e.g. always turn the 2 upside down to represent a 5.

How many digits do you need to represent the numbers from 0-9999? Use any tricks you want, as long as you don't bend or break the digits.


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zex20913
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Is it possible to put one digit on top of another to make a third? I.E, can you put a 1 over/under a 9 to make an 8? That's a trick, but I don't think it's what you meant.

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eytanz
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Yup, you can stack digits on top of each other if you want.

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zex20913
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I do believe I have it!

22 digits. If I'm right, I'll explain my logic. If I'm wrong, I'll keep trying.

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eytanz
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22 is correct.

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zex20913
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Woohoo!

My digits are as follows:

1 0
4 1s
4 2s
4 3s
4 4s
0 5s
0 6s
5 7s
0 8s
0 9s

1+4+4+4+4+5=22

Now, why. Well, the question I had (can you combine them?) allows for a 1 and a 3 to make an 8. If an 8 is in the number, there is a possible 3 places left for other numbers, so it won't discount any numbers. An upside-down, or backwards 2 is a 5. A 3 on top of a 4 gives a 9, which, upside-down, is a 6.

Then, 2 7s will make a 0. You need at least 4 7s to get 7777. The number 7000 presents the biggest problem with these two digits. So, give one 0 and 1 extra 7 and you'll be able to get it.

Thus, all the numbers are possible.

Now, for a new puzzle.

What is the reasoning behind the arrangement of these letters?

BCFHIKNOPSUVWY

ADEGLMRTXZ

JQ

Good luck.

This is actually an original one, or if it isn't I hadn't seen it before.

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Oneiromancer
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The fact that J and Q are off by themselves made me think of Scrabble, for some reason, but that doesn't work for anything else as far as I can see. Just thought I'd mention it though.

Game on,

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DiMono
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I notice that if you space the letters according to where they are in the alphabet, j and q break the rest of the letters up in to groups of 9, 6, 9. Between top and bottom the breakdowns are 5/4, 4/2, 5/4. The top half always ends in a sqaure number. I don't know if I'm on the right track, but that's what I've got so far. Here's my working data:

 bc  f hi k  nop  s uvw y
a  de g    lm    r t   x z
         j      q

a 1	k 11	u 21
b 2	l 12	v 22
c 3	m 13	w 23
d 4	n 14	x 24
e 5	o 15	y 25
f 6	p 16	z 26
g 7	q 17
h 8	r 18
i 9	s 19
j 10	t 20


2,3,6,8,9
1,4,5,7

11,14,15,16
12,13

19,21,22,23,25
18,20,24,26

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zex20913
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You are very far away from the answer I was looking for.

However, I find this extremely creepy and also quite nifty that it turned out this way.

But you are still wrong. Keep trying!

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Schik
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zex20913 wrote:
What is the reasoning behind the arrangement of these letters?

BCFHIKNOPSUVWY

Full abbreviations of elements in the Periodic Table.

ADEGLMRTXZ

Letters in multi-character abbreviations of elements.

JQ

Do not appear in abbreviations of elements.

I'll admit I had to google a periodic table - I had a suspicion but I don't have the table committed to memory.


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Oneiromancer
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Very nice, Schik...I'm ashamed I didn't get it, actually, because I have a fairly sizeable portion of the periodic table committed to memory. Yes, it actually does come in handy several times a week...at least in my line of work.

Game on,

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agaricus5
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Schik wrote:

JQ

Do not appear in abbreviations of elements.

Technically, that's not entirely true. I think for those super-heavy elements with nuclei of size >110 without names given to them, they are using some sort of Latin number scheme, and so any element with a mass number containing a "4" will have a Q in it. However, I think if you ignore this, you're probably right.

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zex20913
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You are *very* close Schik, but Ag is right, there is a q in the lab-mades. Your first line is right, but your descriptions need changing for 2 and 3. It shouldn't take too long from here.

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Schik
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zex20913 wrote:
What is the reasoning behind the arrangement of these letters?

BCFHIKNOPSUVWY

Full abbreviations of elements in the Periodic Table.

ADEGLMRTXZ

Letters that alone aren't abbreviations, however are either the first or second letter in abbreviations of elements in the Periodic Table.

JQ

Do not appear in the first two letters of any abbreviations of elements in the Periodic Table.



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zex20913
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That is close enough to what I was looking for. I'm pretty sure all of the second line starts an abbreviation.

You're up!

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Schik
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There are two fifty foot ropes suspended from a forty foot ceiling. The ropes are twenty feet apart. All you have is a sharp knife with which you can cut the ropes.

Your task is to remove as much of the rope as possible. How do you go about it, and how much rope can you cut off?

Let's assume that there is nothing you can stand on, nobody to help you, etc. - the only things you can use are the ropes and the knife. We'll also assume that you can't jump/fall down from more than five feet off of the floor.


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Scott
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I'm not sure if you consider this cheating.

All of it.

Tie the 2 ropes together.

Climb to the top of one and pull the rope tight so it goes along the ceiling.
Cut that rope at the top and swing down under the other one.

Climb to the top and cut through till it is about to break off.

Climb down. Jump up and grab the rope ripping it down.

DiMono
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Assuming we can jump (and reach) 5 feet in addition to more than 5 feet in height, we can get seventy feet of rope.

Let's call the ropes A and B. Tie a slip knot in B, and start feeding A through it. Climb B to top-20 feet, and pull A taut through the eye in the slip knot of B. Now, with your legs still around B, climb A and cut it at the top. You can now drop A to the ground, descend, and cut 20 feet from B, giving you 70 feet of rope.

Am I close?

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Schik
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Scott wrote:
I'm not sure if you consider this cheating.

Climb down. Jump up and grab the rope ripping it down.

Yeah, I consider that cheating. I suppose I didn't explicitly disallow this.

The only way to make a rope split into two pieces is to cut it all the way through with your knife.

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Schik
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DiMono wrote:
Assuming we can jump (and reach) 5 feet in addition to more than 5 feet in height, we can get seventy feet of rope.

Let's call the ropes A and B. Tie a slip knot in B, and start feeding A through it. Climb B to top-20 feet, and pull A taut through the eye in the slip knot of B. Now, with your legs still around B, climb A and cut it at the top. You can now drop A to the ground, descend, and cut 20 feet from B, giving you 70 feet of rope.

I'm not sure where that 20 feet came from for rope B, but it doesn't matter - you can get more than 70.


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zex20913
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Would you tell us how they are suspended? I.E., is the rope able to be untied at the top?

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Scott
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Are you able to tie knots in the rope while hanging off it? Obviously a knot would have to be lower down than where you are.

TripleM
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Ok, well seeing I just rejoined this forum again, and I love puzzles, believe it or not I read through all 22 pages here.. I've heard quite a few of them before tho. I heard millions of puzzles. In any case, I've also heard this one and can answer your questions..

The rope cannot be untied in any way. Its basically cemented to the roof. No trick there.

Sure you can tie knots in it.

by the way - nobody solved the problem that was on the first page correctly, about the 1 mile or k or watever the unit was, south, west, and north thing. Colour of the bear. All the answers given were wrong..

First of all, if it was the north pole, there are no bears at the north pole anyway. Secondly, there are infinitely many places he could have started in, all *close* to the north pole (and in the same relative place but near the south pole). Consider the place where the "radius" of the earth at that point is 1 mile. Then the 1 mile west would consist of going in a loop - thus one mile anywhere above that loop would work. Similary 1 mile above the place where 1 mile is two loops, three loops, etc etc. All those are legitimate places. The colour of the bear is still white

and oh yeah. its a hoax that einstein made up the "who owns the fish puzzle".

but anyway. I'm here to solve puzzles now..


[Edited by TripleM on 01-30-2004 at 09:58 AM GMT]

Skylancer64
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Actually, you cannot start close to the north pole as a solution. Sure there are circles where 1 mile would travel all the way around the north pole, but the distance from the north pole to the circle is less than one mile. This means that you would have never been able to reach it by travelling one mile south, as the northernmost point of the earth isn't even that far from it. All other circles in which a person would circle twice, three times, in one mile are even closer to the pole. The only solution in the northern hemisphere is the north pole.

This is possible around the south pole though. Start about 1.16, or 1+1/(2pi) miles away from the south pole. 1 mile south will take you .16 (1/(2pi)) of the pole. A east or westward circle will take you all the way around the pole. Then one mile north will return you to your starting point. You can also choose points that will take you twice around the pole, or 3 times when you go west.

However thare are no bears at the south pole. The solution given was correct!

[Edited by Skylancer64 on 01-30-2004 at 12:52 PM GMT]

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Schik
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TripleM wrote:
The rope cannot be untied in any way. Its basically cemented to the roof. No trick there.

Sure you can tie knots in it.

Thanks for filling in there, TripleM. He's of course correct. And while you can't untie the rope at the top, there's no rule against cutting it at the top - I'm not sure what the difference would be.


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trick
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Climb to the top of one of the ropes, cut the other rope at the top, cut the rope you're hanging from at the top as well, and fall towards an uncertain fate at the floor.

If falling towards uncertain fates aren't allowed, keep a small portion of the rope for you to cling to when you cut the rope you're at. Then cut a hole in the roof with the knife and climb through. If the roof is very hard and the knife becomes dull after a couple of days, use your fingernails. If cutting the roof is too cumbersome, go up to the next floor and cut a hole in the floor around where the ropes are in stead (the latter, however, is considered the easy way out, and is frowned upon).

If that doesn't work, bring the roof down by pulling at the ropes, escape before it hits you, and return later to collect the ropes.

Or, of course, you could just throw the knife at the top of the ropes to cut them, but that'd probably be too easy.

Alternately, cut off a portion of one of the ropes, and tie it back so you've got an Y-shape. Hold this, and climb to the top of one of the ropes. Tie the ropes together in a knot in such a way that they cross each other, ie. the rope on the left ends up coming down on the right. Now place the knife above this knot with the sharp side down, tie one end of the Y to the hilt of the knife, and carefully tie the other end to the blade (wrap it around a few times to prevent it cutting too easily). Climb down using the rope not connected to the knife. Now, either catch the other rope when you hit its bend (should be about 10 feet from the floor) and pull, or go down to the floor and jump up to catch it.

Huh, that last one could possibly even work. (Okay, I'll stop now.)

Edit: Eh, forgot that the ropes are 20 feet apart. I guess you could swing... Not that I meant any of the above seriously, of course

[Edited by trick on 01-30-2004 at 01:17 PM GMT]

DiMono
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Cut one at the top, cut the other at the top, bring a parachute.

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