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.
Question
plasmid
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.
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.
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:
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