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How would you cross puzzle land? Part II

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This picks up where How would you cross puzzle land? left off. You've sold your fox, chicken, and grain from the previous puzzle and collected a handsome profit, which you're now eager to go have some fun with. You're on your way to party in the only nearby town, but you find that your path has been blocked. Where there was once a shallow river bed, there is now a river of flowing magma: a volcano has erupted and ruined your route! It would take a very long time to walk all the way around to the other side of the volcano to get around the river of lava, and also a very long time to walk downstream until the river of lava meets the sea to be quenched, so you decide to try to find a way across.

Nearby, you see a bunch of logicians, none of whom are very short. You can tell they're logicians because they're sitting around wearing different colored hats and not saying anything. You also notice that from the time you spot them in the distance to the time you've walked up next to them, none of them have blurted out the color of their hats. You therefore conclude that these logicians aren't exactly the brightest bulbs in the chandelier.

"Hey, can you guys give me a hand" you ask. One of the six logicians sitting outside snaps back, "Bah, we have no time for non-intellectuals like yourself. Bother neither us, nor the rest of our logician group who are inside our headquarters over there." You look toward the building he pointed to, and notice that one of the light bulbs is burned out. Getting an idea, you ask "Tell me, O logician, is the number of members in your group prime, or not?" He looks at you inquisitively and hesitantly replies "Our number is not prime." "Then there are eight among you" you state triumphantly.

There were six logicians outside, and you know from his statement that there are more logicians inside. Since there are not a prime number of logicians, there must be a total of either 8, 9, 10, 12, etc. However, a light bulb is burned out and has not been changed. So there must be a total of 8.

It would take 3 college students to change a bulb: one to hold the bulb and two to spin the ladder underneath him. But it takes three times as many logicians because for every logician who does something, you need two others to sit around with black hats and not say anything.

This is an important point: for those of you who didn't see the first story, you tend to solve problems by being both a little bit of a logician and a little bit of a wise-guy.

Amazed at your deductive powers, the logicians offer to aid your quest to cross the river of lava. One of them offers: "We could dismantle our headquarters and use the planks of wood to build a bridge, although no single plank is long enough to make it across and we have no good means of fastening them together." You take one look at their termite-infested hovel and decline. You then notice a horrid smell and ask them what it is. "Oh, that" one replies "is our garbage heap. We could never deduce a fair way of allocating garbage disposal duties, so it just piled up outside."

NOW FOR THE PUZZLE: You find that each logician (and yourself) can pick up a pile of garbage and dump it somewhere in 1 minute. Each pile makes a 5 foot cube that can serve as a bridge over the lava. But once placed in the lava, such a cube will be consumed after 3 minutes.

You can draw the river divided into 5 foot squares with a number representing how long the garbage placed there has left before it's destroyed. Starting off with no garbage in the river, if you're on the left edge and trying to get to the right edge, you could have a logician set off to dump some garbage in spot X. The picture below shows that a logician is in the process of placing a cube, which will be ready for use as a bridge one minute later.

000000000000000000000000000

X00000000000000000000000000

000000000000000000000000000

Now, using the garbage as a bridge, he can dump some more garbage further in as the original bunch of garbage begins to decay.

000000000000000000000000000

3X0000000000000000000000000

000000000000000000000000000

And continue to build

000000000000000000000000000

23X000000000000000000000000

000000000000000000000000000

On the next round he could try...

000000000000000000000000000

123X00000000000000000000000

000000000000000000000000000

...but if he dumped garbage there, he would then be trapped on the following island.

000000000000000000000000000

012300000000000000000000000

000000000000000000000000000

One more important point: no one can dump garbage on an area of the river that has been filled earlier on: the molten garbage underneath would not be a stable foundation. If you had the situation shown two pictures above this, you could not have someone dump garbage where the 1 is to make

000000000000000000000000000

312300000000000000000000000

000000000000000000000000000

on the next round.

The pile of available garbage is practically infinite for the purposes of this puzzle. The width of the river is 220 feet (= 44 cubes of size 5 feet). You have disposed of the logicians' hats, so you can enlist the aid of all eight of them at once. How would you get across? (There are actually TWO answers that I have in mind, one of which is very logically-mined.)

And finally, to get rid of some of the trivial solutions:

It's too dangerous to try to carry a big load of garbage across cubes sitting in the lava if they're only touching at the corners, let alone trying to jump with it or throw it or pass it around. No one is coordinated enough to dump garbage in the lava in any configuration other than a 5 foot cube. (Definitely not a 220 foot x 1 inch tightrope!) People can't carry out actions instantaneously or within milliseconds or anything – give them a full minute to do their jobs, don't send them across at the very instant a block is dissolving, and don't send them over cubes that are in the process of being placed in the lava: the newly placed cubes won't be ready for use until the minute when they're being placed is finished. (That's why in the pictures above I used an “X” to mean that a block of garbage is being placed here during the current minute and will be ready on the next minute.) The lava will eat small channels in and flow through the bases of the piles of garbage, so you can't build a dam to preserve the garbage downstream.

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Posted · Report post

these puzzles :wub:

I can see a possible solution laying out garbage in a large wedge shape. Maybe. Seeing as how that path looks like a lot of work, I'll go with my strengths and work on the humorous approach.

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Posted · Report post

Here's what I'm thinking in order to get started.

The river is 44 units wide, but I assume infinitely ong for this puzzle. Also, the whole team can place a total of 9 blocks down every minute.

So after 3 minutes, they can make this.

123X0000000000000000000000000000000000000000

3X000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000

Then next round can make this.

0123X000000000000000000000000000000000000000

23X00000000000000000000000000000000000000000

X0000000000000000000000000000000000000000000

Basically, an X would be placed below every 2 so that after a while they can have this path.

000000000000000123X0000000000000000000000000

0000000000000123X000000000000000000000000000

00000000000123X00000000000000000000000000000

000000000123X0000000000000000000000000000000

0000000123X000000000000000000000000000000000

00000123X00000000000000000000000000000000000

000123X0000000000000000000000000000000000000

0123X000000000000000000000000000000000000000

23X00000000000000000000000000000000000000000

The only problem with this is it only gets them halfway. After this last move, they'd require a tenth person to start laying garbage. Either that or they could offset when they put garbage down, so not everyone places the garbage at the end of every minute. I don't know if this would actually solve the problem though. More thinking is required.

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Posted (edited) · Report post

Maybe I missed something, but does the block have to be laid in the lava as soon as it is made or can they make a bunch of blocks ahead of time?

Answer, unrelated to the previous question:

Can I make the garbage into a boat (or a cube) and ride it across the river?

Edited by wafflechip
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Posted (edited) · Report post

just pile the garbage up in stacks like stairs really really high like 400 feet which will take 80 blocks and with 9 people including yourself will take 10 minutes

or you could get a forklift and move the garbage even faster. and will take even less time

then just get a parachute and jump off of it and hopefully the wind will catch you and bring you the 220 feet across the lava and then your done!!

Edited by Dr. Pepper
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Posted · Report post

just pile the garbage up in stacks like stairs really really high like 400 feet which will take 80 blocks and with 9 people including yourself will take 10 minutes

or you could get a forklift and move the garbage even faster. and will take even less time

then just get a parachute and jump off of it and hopefully the wind will catch you and bring you the 220 feet across the lave and then your done!!

You could make the parachute out of the hats! :lol:

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Posted · Report post

You could make the parachute out of the hats! :lol:

I was thinking something similar, though I doubt it would work. Perhaps you could make a large stack of the garbage and push it over all at once?

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Posted (edited) · Report post

I'm working out the logical solution but it goes something like this;

oooooooooooooooooooooooooooooooooooooooooooo

1min

1 x

2

2min

1 3x

2

3min

1 23x

2 x

4min

1 123x

2 3x

5min

1 o123x

2 23x

6min

1 xo123x

2 123x

7min

1 3xo123x

2 o123x

Something along this line. The 2nd row can start later, and subsequently the 1st. Will post it up when I've spent more time on it. Not much time now.

But the funny solution;

Break down the house. Use the planks as a lever. Use a pile of garbage as the fulcrum. Now you've made a makeshift catapult.

I <-you here________x <-put garbage here

-------------------------<-wood

__________o<-garbage (as fulcrum)

Test the range using garbage. To increase the range, change the position of the fulcrum and the numbers of garbage you pile (up to 8) on one end.

When you've got a good range, keep throwing soft garbage to the other bank. Then you fly, and hopefully land on the soft garbage pile. Sure you need to take a bath, but would you rather risk walking on hot lava? :)

Edited by scsw
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Posted (edited) · Report post

This is so simple

42

:P
Edited by JarZe
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Posted · Report post

Here's what I'm thinking in order to get started.

The river is 44 units wide, but I assume infinitely ong for this puzzle. Also, the whole team can place a total of 9 blocks down every minute.

So after 3 minutes, they can make this.

123X0000000000000000000000000000000000000000

3X000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000

Then next round can make this.

0123X000000000000000000000000000000000000000

23X00000000000000000000000000000000000000000

X0000000000000000000000000000000000000000000

Basically, an X would be placed below every 2 so that after a while they can have this path.

000000000000000123X0000000000000000000000000

0000000000000123X000000000000000000000000000

00000000000123X00000000000000000000000000000

000000000123X0000000000000000000000000000000

0000000123X000000000000000000000000000000000

00000123X00000000000000000000000000000000000

000123X0000000000000000000000000000000000000

0123X000000000000000000000000000000000000000

23X00000000000000000000000000000000000000000

The only problem with this is it only gets them halfway. After this last move, they'd require a tenth person to start laying garbage. Either that or they could offset when they put garbage down, so not everyone places the garbage at the end of every minute. I don't know if this would actually solve the problem though. More thinking is required.

That's kinda what I started seeing in my head. It looked like a lot of work, so I left it there. :P

The use of numbers to represent the lava/garbage makes me want to look at binary/base 3 for possible answers.

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Posted · Report post

This is so simple

42

:P

42 what though

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LOL, I really liked scsw's catapult, I hadn't thought of that one! IDoNotExist got the idea behind the humorous solution I had in mind. Notice that I always talked about “cubes” of garbage instead of squares. The fun solution doesn't involve dumping the garbage straight into the lava: instead, we're going to build a tower out of garbage cubes about 5 feet away from the river bank, and then topple it into the lava to get an entire garbage bridge formed all at once! It's just a matter of making the eight logicians build a stack of about 50 blocks of garbage, one on top of the other. They can make a garbage ramp to bring the stuff to the top of the tower if necessary.

But once the tower is built, how do we topple it? Might the eight of them not be strong enough to budge it? Perhaps. If that's the case, I ask one of the logicians to stand next to the pile of garbage, on the side facing the lava river, and start pulling bits of stuff out from the bottom garbage cube. Then it's just a matter of time until... JENGA!!! That's another reason why it's important that the logicians aren't very bright : )

A variant on the theme is to build a tower that's just barely teetering on the edge of collapse, like the ones described in this puzzle. Then send a logician to the top, and have him move far enough out on the top cube to send the tower toppling over. He'd be in for a wild ride, but he should land on the opposite bank instead of into the lava, and he will have created the bridge for me. (Maybe he can get IDoNotExist's parachute made out of hats!)

And there's still a solution that addresses the actual logic puzzle. Hint tomorrow if no one's on the other side by then.

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Posted · Report post

Can we go diagonal?

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Can we go diagonal?

In the last spoiler covering loopholes: It's too dangerous to try to carry a big load of garbage across cubes sitting in the lava if they're only touching at the corners, let alone trying to jump with it or throw it or pass it around.

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In the last spoiler covering loopholes: It's too dangerous to try to carry a big load of garbage across cubes sitting in the lava if they're only touching at the corners, let alone trying to jump with it or throw it or pass it around.

Ah, I should read more carefully.

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[spoiler=Sorry if you dont think im clever :P ]You simply go back home, the party you were on your way to was cancelled due to a volcano erupting.

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[spoiler=Sorry if you dont think im clever :P ]You simply go back home, the party you were on your way to was cancelled due to a volcano erupting.

that gets my vote!

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[spoiler=Sorry if you dont think im clever :P ]You simply go back home, the party you were on your way to was cancelled due to a volcano erupting.

LOL! But you won't want to miss this party; there's going to be a carnival in town for part III ;)

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LOL! But you won't want to miss this party; there's going to be a carnival in town for part III ;)

Oh nice, in that case I better get thinking!

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I know this probably sounds stupid but what if....

You put a bunch of cubes together in a raft shape. Then you could build a giant pole that can touch the bottom of the river. Or you could use the poles to push of the banks. Also you stack extra cubes on your raft so that once you can't push with the pole anymore you can make a path.

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All you people who want to pilot a boat of garbage across a river of lava sure are brave! But as the saying goes, it's so crazy it just might work.

At any rate, I guess it's time for that hint I promised earlier.

Three cubes in the lava.

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

That's why I had to be very careful how I phrased my response to scsw's question on whether you can go diagonally. Technically, you can.

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Not much action since the last hint, so here's another hint.

A slug was sitting in the bottom of a well. One day he crawled up 3 feet. At night, he rested and slid back down 2 feet, so the following morning he was 1 foot up the well. The second day, he crawled up another 3 feet and slid back down another 2 feet that night, so after two days he had netted two feet. How long did it take to make it out of the 30 foot deep well?

Spoiler for Answer:

It took 28 days. After 27 days he had made it 27 feet up, so during day number 28 he crawled 3 feet up to make it out of the well and was done.
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All you people who want to pilot a boat of garbage across a river of lava sure are brave! But as the saying goes, it's so crazy it just might work.

At any rate, I guess it's time for that hint I promised earlier.

Three cubes in the lava.

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAA

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

AAAAAAAAAACCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBBCCCCCCCCCC

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

BBBBBBBBBB

That's why I had to be very careful how I phrased my response to scsw's question on whether you can go diagonally. Technically, you can.

Ah I see your trick now. From your diagram in the OP using 0, 1, 2, 3 and X, it was very misleading. It implied that you could only place cubes within that grid shape because that's how it was drawn, but I guess it was never explicitly stated.

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Maybe this hint will open some more possibilities.

Although I'm looking for a solution that's mostly logic-based, that doesn't mean that it's completely without tactics that are less than scholarly.

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Garbage burns too fast...

How long does it take for a logician to sink into the lava? According to Brainden, we've got way too many of them anyways.

And if we run out, any Swindlecants lying around?

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Just how much garbage does one logician spout per minute? This must be how they accumulated so much. Ask a few of them how they would cross the lava river. When the garbage starts flowing, just point them in the right direction and try to follow along.(This shouldn't be too hard since they're not that bright.)

The path will meander a bit, but eventually they will get you where you need to go. Just be careful not to derail the train of thought or you're all doomed!

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