Pirates and a Rope Bridge (July '22 Challenge Question)

I think you got the best possible time (GA). What I can add is only that you have the same result if A returns first and C second.

The radius of the torch illumination is not given. It is reasonable to assume it is 9/10 the span of the bridge, because that would allow John (10 min.) and Anne (1 min.) to safely cross simultaneously. Accepting this, then a possible scenario is one person standing at the centre of the bridge, holding the torch to illuminate the bridge walkway for the others, one at a time, to cross.

So, with John and Billy starting together, John (10 min.) carries the torch and stops in the middle while Billy (5 min.) continues to the other side. Elapsed time 5 minutes. Then Anne (1 min.) crosses by the light of John's torch. Elapsed time 6 minutes. Charles (2 min.) then begins to cross. At the moment he starts, John also starts walking from the centre to the other side. This takes him 5 minutes, and in that time Charles has passed him and is already on the other side. Total elapsed time 11 minutes.

By that time,the buccaneers have caught them.

Even better:

With the reasonably assumed torch illumination of my previous post, John (10 min.) and Anne (1 min.) start together across the bridge, with John carrying the torch. When Anne reaches the other side, Charles (2 min.) starts, his path being lit by John's torch. When Charles reaches the other side, Billy (5 min.) starts, his path also being lit by John's torch. Anne, Charles, and Billy are safely on the other side when John, with the torch, arrives. Total elapsed time 10 minutes.

You mean that one is allowed to assume about the torch?

A "Torch" is sometimes used to refer to a flashlight,not necessarily a fire on a stick.

I am aware of the two meanings of "torch", but since the bridge problem takes place in the age of buccaneers, when there were no flashlights, the referenced torch must be a fire on a stick. A fire on a stick casts a circle of light. What is the radius of that circle? By reasoning, and not just by arbitrary assumption, the radius of the circle of light must be at least 9/10 the span of the bridge. Why? Because as set forth in the problem any two people can cross the bridge together. No limitation is stated as to how they can pair up; and also, by strict interpretation of the specifications, each must walk at the speed assigned to each. Obviously if John (10 min.) the slowest, carries the torch, and walks with Anne (1 min.) the fastest, they will not be walking side by side. Anne will be across the bridge when John is only 1/10 of the way across. But the torch will safely illuminate Anne's traverse of the bridge. The problem description states this. Therefore the radius of illumination of the torch must be at least 9/10 the span of the bridge. This enables the two solutions I posted. In both solutions only two people are on the bridge at any one time. My second (10 minute) solution is preferred because in that solution all four people remain in constant motion, at the specified speed of each, crossing the bridge in the direction of escape.

Explain your reasoning for the distance of the light illumination,not assuming anything.

The original question did not specify that no one could carry another one across,that would be speculating or assuming what is not specifically stated.

One could also assume it was the Tampa Bay Buccaneers that were chasing them,which turns the flashlight assumption back on.

My answer is simple and assumes no more than yours,and I will never argue with you.

Your quote: "Explain your reasoning for the distance of the light illumination."

I fully explain my reasoning in the post to which you are responding (Post #9).

My assumptions are no greater than yours,still within the specs of the question,and mine is simpler and quicker.

You are free to accept your definition,I will never argue with you.

There is nothing in the problem specs from which you could reason that the torch can illuminate the entire span of the bridge, as you do in your Post #2. Further, there is nothing in the problem specs from which you could draw any conclusions about the weight and strength of the four individuals, as you also do in your Post #2. Everything about your "solution" is based on unsupportable, arbitrary assumptions.

My two solutions, by contrast, emerge from one and only one statement - that the torch can illuminate 9/10 the span of the bridge. That statement is reasoned from the problem specs, as I fully explain in Post #9. If you see a flaw in that reasoning, please present it.

DANG IT!

I forgot! It could be the Pittsburgh Pirates that could be chasing them.

If we are free to assume anything,then we are free to assume everything that is not explicitly denied in the original question.

Think outside of the box,within the stated parameters,and a lot is possible.

The challenge could be more explicit in how the bridge had to be crossed.

I have noticed that my editied replies are always redirected before posting.

Also the server is verified.

Is this a new security feature?

The specification is that the individuals CAN walk at particular speeds, not that they must. There is no reason to assume that the torch can illuminate any more than a few paces forward

Your post is almost identical to Alex. Roman's #17 Post, so my response (see Post #21) is also identical. If you were being pursued by buccaneers and you could cross the bridge in one minute, would you choose instead to cross in ten? My solution reasonably assumes that all four would move at their maximum specified speed, and consequently would not walk/run side by side, and this raises the question of the radius of the torch illumination, which from the problem specifications can be deduced. It is a more creative, interesting approach to the solution than the obvious, conventional, and boring back and forth shuttling solution described here by others. My solution is in accordance with the defined problem, and gets them all across the bridge in the shortest time.

My solution gets everyone across the bridge faster.

It is what I would do if I was being chased by Pirates of Buccaneers.

No need to shuffle back and forth,and it is much quicker than other methods.

What would you do,seriously if you were being pursued by Buccaneers or Pirates?

Think about it.

I will see you on the other side,if you don't get captured.

I will never argue with you.

Call your next case.

I'm moving on.

I have to cut a Gordian Knot.

This is the 2nd time you have argued with him. Admit it.

Part of the specification is that the 4 individuals all cross as a group. It is not the quickest time for an individual being asked for but a total group time. If this involves one individual moving slower than they otherwise could, then so be it.

No, it does not specify they cross as a group. It specifies that "The bridge can only hold two people at once."

If a solution is in accordance with the specifications, then it is a valid solution:

1) It is specified that only two can be on the bridge at any one time, but no restriction is placed on who can pair with who. Implicitly, it is also allowed that only one person be on the bridge at any one time.

2) It is stated that each individual either can cross in a specific time or needs a specific time to cross. Implicitly therefore, the solution could utilize any time up to and including the given time for each.

3) It is not specified that when two people are on the bridge together the faster individual must slow his or her pace to match that of the slower individual, therefore the solution may or may not include this speed adjustment.

4) It is not specified how far the torch casts its light, however it can reasonably be concluded that it is of sufficient brightness to permit any solution that uses any combination of variables set forth in the foregoing points 1, 2, and 3. Therefore if, for example, John (10 min.) pairs with Anne (1 min.) and each, as permitted in the specifications, move at their maximum pace, the torch must be of sufficient brightness to enable this allowed variable. Specifically, the circle of light cast by the torch must have a radius of at least 9/10 the span of the bridge.

My solution (post #6) is in accordance with the problem specifications. Here it is again so that it is in the same place as the above reasoning:

John (10 min.) carries the torch and starts out with Anne (1 min.). John has travelled only 1/10 the distance across the bridge when Anne reaches the other side, but his torch has safely illuminated her way (as per point 4 above). The moment Anne reaches the other side, Billy (5 min.) starts. He passes John and gets to the other side, his traverse also safely illuminated by the light of John's torch. John is now 6/10 of the distance across the bridge. Charles (2 min.) immediately sets forth. He too passes John, safely illuminated by John's torch. John is 8/10 the distance across when Charles reaches the other side. It takes John another two minutes to get across, for a total elapsed time of 10 minutes.

...and that is how all four got safely across the bridge in ten minutes. When the buccaneers arrived at the bridge crossing they pulled up in surprise. The four desperadoes were gone. The captain snarled, "Bend your ears, maties. They can't have got far. The clump of that peg leg will carry for half a league in this canyon." So they listened, and they listened... But all they heard, just like here, was the sound of crickets.

(Gee, I wonder who was the we-don't-like-your-kind-around-here-good-ol'-boy who voted my solution 'Off Topic' ?)

I will never argue with you.

You are the greatest!

Thanks for the praise. Since you are afraid to argue with me, I invite anyone else here to do so on your behalf. If someone here can identify a flaw or flaws in my Post #42 reasoning and solution then please point it/them out and explain. I was careful not to make any assumptions, only reasoned deductions, so a reasoned response if you choose to respond would be appreciated.

No fear,just dignity.

I seldom stoop so low.

It is like trying to argue with one of my grandchildren.

So simple minded and naive at that tender age.

I am ashamed that I have given in to the boredom.It is beneath me.

I only reply out of sheer boredom,and I find you slightly less boring than watching haircuts or a puddle drying up.YAWN!

I think I will go count the particles on the ceiling,ad follow the fan blades around on low speed,then advance to high speed so I can go to sleep.---zzzzzz---

Your motto should be: When my bag of arguments is empty, my bag of insults is always full.

Agreed. it's reasonable to assume that any of them can walk more slowly than their maximum speed, but not that they can seperate and still use the same torch.

As in real life, the devil is in the detail

"As in real life" you write. Well, in real life I am sure you have walked with someone at night, carrying a torch/lantern/flashlight wherein it was not necessary for you both to walk shoulder to shoulder to keep within the light. The magnitude of the circle of light cast by the torch is not specified in the problem, therefore it is an arbitrary assumption that the light circle is so small that two people must walk shoulder to shoulder, and the resulting solution is no more valid than one based on an assumption that the circle of light is, say, fifteen feet in diameter (or to make it solvable, a specific fraction of the span of the bridge) and which would enable two people to walk at a distance from each other.

I disagree. Since they are being pursued by buccaneers it is more reasonable to assume that if each of the four individuals can cross the bridge at maximum speed, they will. In my Post #6 solution (10 minute total elapsed time), all move continuously at the maximum given speed, and only two are on the bridge at any one time. I assert that this is possible because the circle of light from the torch has a radius of 9/10 the span of the bridge, and that this assertion can be directly deduced from the problem specs (explanation in Post #9). I submit that this is a more creative and interesting solution than the typical, boring, back and forth shuttling of the four people which is described elsewhere in this thread. I do not share other posters' enthusiasm and praise for that conventional approach to the problem.

#2 off topic? The question did not specify anything except the bridge,people and the time of each,and that the light be shared.That left anything else up for interpretation.

A challenge question should be specific.

I believe in K.I.S.S!

Obviously Billy has the gold, he grabs Anne and crosses the bridge, Charles and John set fire to the bridge as they cross, and do their best to get across before it collapses...the fire will light their way...

Your imagination is illuminating.

In the real world,Anne is very greedy.

She grabs the gold and crosses the bridge alone, (no one can catch her,she is too fast) then she burns the ropes to the bridge so no one can follow her.

Anne is now living a life of luxury on a private island in the tropics.

The others are captured and made to serve out their lives on the pirate ship as slaves,taking turns in the barrel.

She got the gold,the rest got the shaft.

This seems plausible, as we have to assume that the weights of all the participants are approximately equal, Billy must be a lightweight because even carrying the gold his weight is equal to Anne's, and Anne must be a stout girl....If we assume a median weight of 185 lbs each, and we have 50 lbs of gold, Billy only weighs 135lbs, which would explain his 5 min struggle to cross the bridge...

Gimme that gold....

I agree with Randall.

People with gold being chased by anybody will always get the gold across first and as many people as soon as possible. It is not reasonable that Ann can carry Billy and the gold in 1 minute. It is not reasonable that the torch shines all the way, so here is my solution:

Ann & Billy & the gold - 5 minutes

Ann back - 1 minute

Ann & Charles - 2 minutes

Ann back - 1 minute

Ann & John - 10 minutes

Total time - 19 minutes (assuming the chasers have not caught up).

But people do not always do as expected, so after Ann goes back the first time, she rests while Charles carries John:

Ann & Billy & the gold - 5 minutes

Ann back - 1 minute

Charles & John - 2 minutes

Charles back - 2 minutes

Ann & Charles - 2 minutes

Total - 12 minutes

Given the current women's world record for 400 metres, and Anne's 1 minute time to cross the bridge, 400 metres is the approximate maximum span of the bridge. If it takes Charles 2 minutes to run across the 400 metre span it indicates that he is not in good shape. It is therefore not reasonable to suppose that Charles could carry John that 400 metres and still maintain his two minute time. This criticism applies to the other one-person-carrying-another scenarios presented in this thread.

Of course if Jack Sparrow was involved:

Anne and Charles would cross first, with Anne slicing through the ropes connecting the "hand rail" rope to the treads just behind them (she has plenty of time: she's twice as fast as Charles).

John and Billy would tie thememselves to the near end, and, as soon as the other two were across they would cut the bridge at their end and swing across. All across in just over two minutes, and, the chasing team cannot reach them.

Now in order to comply with the "rules", Anne and Charles drop the torch to Billy; he ties the gold to the hand rail rope, which the others pull up; they then drop the rope again and help Billy to climb up; they then drop the torch and rope again to John, and the three at the top pull John up.

They've crossed the chasm/bridge in just over two minutes, and are able to carry on together.

I like this solution more than your conventional solution presented earlier. The assumed possession of two knives is in conflict with the problem specs, but it is probable these desperadoes would have knives, so it is plausible - certainly more plausible than the one-person-carrying-another-to-save-time scenarios presented here by others. Two quibbles: You didn't allow enough time for the tying and untying of ropes. Also, Billy and John, to free their hands for the rope tying, would have to hold the torch in their teeth, but that's okay.

I like that;thinking outside of the box.

The original poster of the challenge should "'illuminate" this forum with the correct answer(s),please.

Certain individuals,which shall remain nameless,but they know who they are,can allow assumptions to validate their method(s) buy disallow all others to make an assumption of any type.

In a well written challenge,exclusions should be clearly stated.Since the challenge did not define any exceptions,then all interpretations are valid.The challenge did not specify a certain era in which this event occurred,so that opens the door to even further interpretations.
Their are modern day pirates,so it is possible that the events are occurring in the current era,which opens the door to many possibilities.

Of course,these obvious exceptions will be excluded by some respondents, in order to defend their flawed analysis,and will squirm like a worm in hot ashes if their exceptions and opinion are challenged.

(There is a big difference between "Can" and "Must".)

That is why I appeal to the originator of the challenge to reveal the real solution(s),to settle the dust.

I personally don't care what the answer is,because I have no ego-equity in the answer.

Your quote: "Certain individuals, which shall remain nameless, but they know who they are, can allow assumptions to validate their method(s) but disallow all others to make an assumption of any time."

Your Post #2 (assumption free) solution: "Anne can carry John across,she is very strong,and John is very light. Time:1Minute Anne shines the light back across the bridge to illuminate it for the others.The light is very bright. Charles,being a weight lifter,and flooded with adrenaline, can carry Billy who is also very light, across with no time lost. Time: 2 minutes. Total time:3 Minutes"

As the world turns,the worm squirms.

Interesting that in this forum, populated by people trained in the analysis of problems, no one acknowledges that the magnitude of the radius of light cast by the torch directly affects the solution, nor acknowledges that the omission of this specification from the CR4 version of the problem makes it a different problem than the one posted on YouTube.

If the torch cast a circle of light, say, 12 feet in diameter, it would still be in accordance with the statement, "There is only one torch between them, which they must share to safely walk across," (unless the bridge is only 6 feet long), but it would be a different problem then the problem you solved in which you arbitrarily assumed a circle of light about 3 feet in diameter. It would be a different problem because the person carrying the torch could stop short of the end of the bridge in both directions, and the solution to that problem, with its arbitrary assumption of a 12 foot circle of light, would be as valid as the one you posted.

You are being silly. I am being rational. CR4 replaced the YouTube specification that "the old lantern you grabbed on your way only illuminates a tiny area" with the specification that "there is only one torch between them that they must share to safely walk across". The CR4 specification is vague. It makes no reference to the radius of the circle of light cast by the torch. Provided that radius of light is less than the span of the bridge, then any two people simultaneously crossing the bridge would necessarily be required to share the light of the torch to safely walk across - and this would meet and be in accordance with the CR4 specification. Consistent with this reasoning, any arbitrary choice of light radius, less than but not equal to the span of the bridge, would form a distinct problem with a distinct solution. However, I argue in my post #42 that there is sufficient information provided in the CR4 version of the problem to make a reasoned, not an arbitrary, choice of light radius, and the solution associated with that choice is preferred.

Likely the NC is afraid to give the "correct" answer because of reprisal from you. Nice going.

Don't know who or what NC is, but if 'NC' posted this challenge maybe NC changed the wording deliberately to add a subtle logical twist to trip up those who are already familiar with the problem.

Anyone that is afflicted by NPD is to be pitied,not chastised.

Philosophunculist's are frequent sufferers of this affliction.

I feel is was good question because of the number comments and replies that made me laugh

Just as a segue the pictured bridge is

THE CARRICK A REDE ROPE BRIDGE

In Antrim Northern Ireland

In the 1970's fishermen crossing the bridge carried a change of underwear and a roll of toilet paper as standard fare.

Anne acts as the torchbearer. She takes the torch and moves forward to such a distance where the torch beam could be reversed to guide the next crosser . She does this till the next one crosses . She then does the same exercise with the third member and so on, till all have crossed .

She could even carry the gold bag and cross first, leave it unguarded of course and return to guide the crossers, if the weight of the gold bag is substantial .

Here is what can be logically deduced from the Given conditions:

Anne crosses the bridge in 1minute.The average walking speed is 3 MPH,but given that she is being chased,4mph is not unreasonable.

At that rate of travel,in 1 minute,she will have traveled 352 feet,hence the bridge is 352 feet long.

If she places the lamp at mid-point,that will divide the illumination equally between both ends,and gives an illumination circumference of 176 feet,thus the lamp is equally shared.

The next fastest person(Charles) picks up and carries the slowest person(John),because the peg leg may get stuck in between the planks) across the bridge.

This is not excluded in the challenge,so it a viable conclusion.

If it were excluded,it would have stated that no one can carry another,instead,it said that only 2 may cross at the same time,not how they must cross.

The fact that John has a peg leg is significant in solving the puzzle,or it would have simply stated that he was slower than the rest.

Hence: Anne=1 minute@4MPH

Charles,carrying John,crosses in 2minutes,2 MPH,only half of Anne’s Speed

Billy crosses in 5 minutes (since he is carrying a very heavy bag of gold.)

Total time 8 minutes.

I don't agree with your assertion that someone who can cross the bridge in a certain amount of time, can match that time while carrying someone else, but, if we accept that and your other assumptions then you can reduce your 8 minutes to 7 if Billy sets off at the same time as Anne.

Anne is filled with adrenaline,and does not even feel the weight on her shoulders,and would be moving at more than 4mph if not loaded.

Ordinary people do extraordinary things under duress,such as picking up cars at a wreck scene, trying to outrun a bear,etc. so I think my assertion is valid.

Of course,opinions vary,and there can never be a valid argument in matters of opinion or taste.

It takes 2 horses and two people to make a horse race.

Different opinions drive the stock market,and the entire world economy as well.

If everyone had the exact portfolio that they wanted,and never sold it or bought anymore,the stock market would crash.

I respect everyone's opinion,even if they fly in the face of logic,and I don't agree.

My disagreement does not mean they are wrong or that I am right,it is simply an opinion,like everyone else's.

To each his own.We are all in this together.

The most valuable and rare commodities in the world are peace and tolerance,peace above all.

I think that would violate the conditions set forth in the challenge:

'"...only 2 people... "

Not necessarily the room on the bridge,but the load capacity of the bridge.

Of course,the point loading on the bridge could be exceeded by Anne with her load,but I am ignoring that because the challenge did not address that matter.

For that matter,Anne could also carry the gold and John,allowing Billy to cross faster,etc,etc.

Many possibilities are not specified in the challenge,that is why I said it was poorly written in a previous posting,and leaves many avenues unexplored.

I was replying to your post #68 in which Anne crosses on her own.

You are correct.My bad.I should have worded my reply more precisely to reflect my thoughts.

"There is only one torch between them which they must share to safely walk across."

This does not mean that they could not cross the bridge without sharing the torch, only that doing so would be unsafe. Analogously, molten metal cannot be safely poured without wearing protective equipment. It can still be poured, just not safely. We know that the four have little concern for safety, because stealing gold from buccaneers is not a safe thing to do. Therefore the problem specifications about the sharing the torch, and the safety associated with that, can be ignored.

We can deduce from the specifications that the bridge has a sign that reads, "Load capacity: Two People". But Anne had studied structural engineering at the University of Glasgow (the first woman graduate in the field at that time), and she knew that bridges always have a safety factor. Therefore she told everyone to ignore the sign. She said if they spread out as they crossed there would be no problem. She needn't have given that advice because since they each moved at different speeds (1, 2, 5, and 10 minutes) they spread out and distributed their weight as a matter of course. This is the reason the problem specifies the various times for each.

So they all crossed the bridge together. Those who were too far from the torch light continued unsafely at their normal pace. Total elapsed time 10 minutes.

Here I present the fastest solution of 150 seconds:

1. The fastest pair of Anne and Charles crosses the bridge, with the torch. This takes 2 minutes.

2. The slowest pair then step on the bridge and cut the ropes, while holding onto the bridge for dear life. The bridge falls and becomes a ladder, hanging on the other side. At this point in time they have already crossed the canyon, total time is the two minutes of the first pair, and say 30 seconds of the second pair (stepping, holding on, and cutting the ropes).

3. The first pair drops the torch - the second pair catches it

4. Johnny and Bill climb up, Johnny perhaps assisted by Anne and Charles, pulling him up.

Since everyone has crossed the canyon after step 2, and "time until they are safe from the buccaneers" is the Key performance Indicator, I can ignore the climbing time :-)

OK,if you want to go Way out of the box:

All 4 of the people were part of a circus act where Anne carries all 3 men on her back,while walking a tightrope over a pit of alligators.

They are being chased because the circus hired the buccaneers to retrieve the gold that they stole from the circus coffers.

Crossing the bridge in 1 minute is easy for Anne,compare to the circus act.

Time for all to cross: 1 minute.

Anne filed a lawsuit against John for sexual harassment ,because of his peg leg hitting her below the belt when she was walking.

She said he did it on purpose,but he said it was unavoidable at the rapid pace she was walking.

She also said she didn't like where he put his hands,but he said the had to hold on to something so he would not slip off.

The trial has been postponed to a later date many times over the years,and even today, it is still pending,and will be until all of the gold has been taken by the lawyers for fees.

That's Life!

"It's like déjà vu all over again."

In post #32 Randall posits an almost identical fanciful solution. His and yours assume the span of the bridge is shorter than the depth of the chasm/canyon. But if the bridge is, say, 200 feet long and the chasm/canyon is 100 feet deep... well, you can visualize the outcome.

I love the sense coming through