Maximizing Bridge Capacity: A Weight Distribution Dilemma

[iknownothing]

My first post... So be nice, or I'll blast you with a phaser...

You are at one side of a canyon at the start of a bridge. The only way to cross the canyon is over the bridge. (no tricks to this, just a normal crossing of the bridge, don't try to walk on water here) On you side are 3 gold bars, each weighing 3kg. You weigh 78kg. The bridge can only support 80kg without breaking. How do you get yourself across with your new found wealth, without falling through the bridge?? --And no, you can't throw it across.

 

[shibumi]

as far as the question goes i know that it has to do with applied force and kinetic energy but the math is beyond me.

 

[Galileo]

You wait until you weigh an ounce.

...or at least 7 kg lighter. Then go across with the gold bars.

 

[shibumi]

true enough but i think that there is an impetus of time involved? where the person needs to be across within a certain time frame that doesn't allow one to wait until they are emaciated. good try! :)

 

[marcus]

My first post... So be nice, or I'll blast you with a phaser...

You are at one side of a canyon at the start of a bridge. The only way to cross the canyon is over the bridge. (no tricks to this, just a normal crossing of the bridge, don't try to walk on water here) On you side are 3 gold bars, each weighing 3kg. You weigh 78kg. The bridge can only support 80kg without breaking. How do you get yourself across with your new found wealth, without falling through the bridge?? --And no, you can't throw it across.

break up the gold bars into smaller chunks and make several trips
each time taking a chunk weighing less than 2 kg

 

[matthyaouw]

Go round?
either that, or put the gold bars in your bag, cut the ropes of the bridge, and swing across indiana jones style, before undertaking a daring climb up the other side.

(in other words, I havn't the foggiest idea!)

 

[tribdog]

I think I've got it.tie a rope to the bricks, walk across the bridge then pull the bricks across..

 

[albengineer]

so what is the answer?

 

[tribdog]

so what is the answer?

I gave it in white letters in the post above yours. you have to select it to see it.

 

[Moonbear]

Nah, I think this is the answer (in white text):
You have to perfectly synchronize your jumping (or hopping) across the bridge with your juggling of the gold brick so that you aren't touching the brick when you're touching the bridge. You better practice it a bit before trying it for real, it would require immense coordination.[/color]

 

[bjr_jyd15]

I'm sure if you can induce enough vomit you can lost a kg. Then make trips with one gold bar at a time. But be sure to brush your teeth afterwards.

 

[Dual Op Amp]

Maybe...
Take off all your clothes, then walk with one bar at a time.

 

[DaveC426913]

Not sure if you were serious tribdog, but this won't work:

"...You have to perfectly synchronize your jumping (or hopping) across the bridge..."

If you could actually decrease your weight by continually jumping, a lot of people would be doing it instead of dieting. Your weight will far exceed 80kg every time you land.


Personally, breaking the bricks in half is the most plausible solution. This problem doesn't indicate if you can use props, like tools to chop, melt or otherwise dissassemble anything. Just seems a little simplistic for a puzzle.

Then again, if you can use props, the rope trick would work just fine.

 

[tribdog]

Not sure if you were serious tribdog, but this won't work:

"...You have to perfectly synchronize your jumping (or hopping) across the bridge..."

If you could actually decrease your weight by continually jumping, a lot of people would be doing it instead of dieting. Your weight will far exceed 80kg every time you land.


Personally, breaking the bricks in half is the most plausible solution. This problem doesn't indicate if you can use props, like tools to chop, melt or otherwise dissassemble anything. Just seems a little simplistic for a puzzle.

Then again, if you can use props, the rope trick would work just fine.

I wasn't the one who came up with that solution. That was moonbear.

 

[Moonbear]

Not sure if you were serious tribdog, but this won't work:

"...You have to perfectly synchronize your jumping (or hopping) across the bridge..."

If you could actually decrease your weight by continually jumping, a lot of people would be doing it instead of dieting. Your weight will far exceed 80kg every time you land.

But in the puzzle, my weight alone is only 78 kg, not 80 kg. Do you think the puzzle would take into account real physics? I wasn't reading that deeply into it.

Though, actually, continually jumping is an excellent way of losing weight. If more people jumped continuously, they wouldn't need to diet!

But, aha! Working together can help sometimes...maybe the solution is to jump around for a while, run back and forth the bridge a few times, pee, whatever, until you've lost a kg, then you can just walk across carrying the gold with no problem.

Then again, no gold is worth walking across a bridge with a weight limit within only 2 kg of my weight! I want to see those error bars first!

 

[marcus]

break up the gold bars into smaller chunks and make several trips
each time taking a chunk weighing less than 2 kg

when I suggested this back a ways in post #5 of this thread, i didnt think anybody would be wondering how you'd break a gold bar in half-----if you found one in a canyon

canyons have rocks. I'd put the bar between two rocks and chop it in the middle with a third rock.

how big is a 3 kilo gold bar?

gold is 19 times denser than water so the volume of a 3kg bar is about 1/6 of a liter.

that is less volume than an ordinary kitchen measuring cup

and gold is soft, so I think that volume of gold formed into a bar
would be something you could hack or bust in half without too much trouble


warn moonbear not to jump on a fragile bridge

 

[Moonbear]

and gold is soft, so I think that volume of gold formed into a bar
would be something you could hack or bust in half without too much trouble

Well, if you can hack it or bust it in half in the middle of the woods, surely you can also stretch it into a very fine wire, long enough to make about twice the length of the bridge. Grab one end, leave the other end behind and you have no more than half the weight of the brick with you on the bridge when you are at the other side. Then just pull the rest across. On the downside, be very careful not to get a tangle in the wire, or you'll drag the whole clump onto the bridge and fall to a horrible death.

warn moonbear not to jump on a fragile bridge

Aye aye cap'n!

Out of curiosity, how did I get to the side of the bridge I'm on anyway? I have to cross the bridge to get to the other side of the canyon, but is that the right direction to get home? Maybe all I need to do is grab my three bricks of gold, toss them in my backpack, and turn around and walk back out the way I came from.

 

[tribdog]

One time I was out camping and when dinner time came I grabbed a can of chili then realized I didn't have a can opener. I beat the hell out of that can trying to open it. That can got the best of me and I had to settle for chips for dinner. My point is: you can't break a bar of gold with a rock. Go grab a rock and break a silver dollar in half and I'll believe you could break the gold.

 

[iknownothing]

Sorry Guys and Gals,


I really don't have an answer to this one. I put it here hoping to find a physics answer. But I like the one saying don't cross the bridge, just walk the other way.

...Then again, could you create a rope to drag the bricks by pulling pieces of the bridge off? ...I've never made rope, but I'm sure I could if there were 3 gold bricks wanting me to!

 

[Moonbear]

One time I was out camping and when dinner time came I grabbed a can of chili then realized I didn't have a can opener. I beat the hell out of that can trying to open it. That can got the best of me and I had to settle for chips for dinner. My point is: you can't break a bar of gold with a rock. Go grab a rock and break a silver dollar in half and I'll believe you could break the gold.

First you need to find the right type of rock, then find another rock, and chisel the rock into a spear point, try not to smash your fingers with either rock or cut your hand open on the sharp edges, then, no problem, you have a can opener. I used to carry around one of those 10 cent can openers you can buy in army surplus stores that goes on your keychain. Stopped carrying it when they banned anything with a point on it from airlines since I fly a lot and would forget to take it off the keychain. You'd be amazed how often you find yourself in the middle of the woods in need of a can opener. You could have tossed the can on the campfire and when it exploded, then retrieve the chili...just don't stand too close when you do that. I hear chili can shrapnel really burns!

 

[Moonbear]

Sorry Guys and Gals,


I really don't have an answer to this one.

I put it here hoping to find a physics answer. But I like the one saying don't cross the bridge, just walk the other way.

Well, since that was my answer, okay, I'll forgive you for sending us a question with no known answer.

 

[GCT]

Be practical, throw it across (in acknowledgment of this reference in the first post).

 

[marcus]

One time I was out camping and when dinner time came I grabbed a can of chili then realized I didn't have a can opener. I beat the hell out of that can trying to open it. That can got the best of me and I had to settle for chips for dinner. My point is: you can't break a bar of gold with a rock. Go grab a rock and break a silver dollar in half and I'll believe you could break the gold.

If you can bend it back and forth, then you can break it.
Metal fatigue.

I am pretty sure i can break a silver dollar with pliers. by bending it back and forth several times

but with a bar of gold, I count on it being longer. so I can use cruder tools to bend it this way and that, until it breaks

 

[Astronuc]

9kg of gold at ~$450/oz (near current futures price) = $142,857 or $47,619/bar. Pretty serious incentive to get across the bridge, and presumably to the nearest bank, commodities broker, or precious metals dealer.

Actually a similar problem had one tie rope to the load, lower the bars to the bottom of chasm (assuming rope long enough to reach down to bottom of chasm, but not long enough to reach across the bridge), cross bridge (hopefully with less than 2 kgs of rope) and pull load up other side. Otherwise, if rope longer than bridge, tie rope to bars, cross brigde and pull bars with rope over bridge. Maybe one needs to fashion a cart or litter to hold the bars.

Certainly one could remove 1 kg of clothing and carry each bar across, if there is not a constraint on the number of trips.

But what if one does not have a rope. Well bury the gold and return later with a rope.

Or just use one's cell phone, which everyone seems to have, and get a helicopter to pick one up.

 

[tribdog]

I held a bar of gold once. It was about 80lbs. no way I could have busted it. I'm pretty sure that my original answer is the correct one and the question was probably written wrong.

 

[Moonbear]

I held a bar of gold once. It was about 80lbs. no way I could have busted it. I'm pretty sure that my original answer is the correct one and the question was probably written wrong.

Actually, it's hard to find gold bars even 1 kg. Most that are commonly available are far smaller than that. Which means you're hallucinating the whole thing, the bridge doesn't really exist, and if you try to cross it, you're going to fall into the gaping chasm.

 

[vikasj007]

i think we are missing some basic facts here.

first, how do we know that the gold bar is actually pure gold, and the more impure it is, the harder it is to break it.

secondly, how did three gold bars weighing exactly 3 kgs, come there, obviously someone must have lost it. if so, why did he not come back for it.

also, if someone dropped them, then the way that he did not notice it, would be if he was carrying a large no. of bars. in that cas3e, how did he cross the bridge. if he used some other route, why not use the same.


and we know that he has not fallen into the canyon, as nobody would be supid enough to commit suicide, wtih that amount of gold,( i assume that he had far more gold than 9 kgs) and if he fell into the canyon trying to cross the bridge, then the bridge would have collapsed, which is not the case here.

so this problem has far too many problems(errors) to be solved.

 

[iknownothing]

Ok, as I said in the first post, ... no tricks to this. This problem has mathmatical and physics type answer. I figured I could find somone ingenious enough here to give me that. I guess I'm wrong.

 

[tribdog]

you've gotten several answers. What did you expect? We gave as good of answers as MacGyver could have come up with.

 

[Moonbear]

you've gotten several answers. What did you expect? We gave as good of answers as MacGyver could have come up with.

No we didn't! You forgot the duct tape! MacGuyver doesn't do anything without duct tape...or was that the A-Team?

 

[ascky]

Well it depends how you define supporting '80kg without breaking'...

If you're standing close to one side of the bridge, you'll be exerting more force on the side you're closer to. But if you stood in the middle of the bridge, the force would be shared equally between the two endpoints of the bridge...

Assuming you can jump to the middle holding your gold bar...?

Don't know if the math works out

 

[ascky]

Actually if the elevation up to the bridge was right, couldn't you get the middle of the bridge close to the turning point of the parabolic jump? Would that help...? Confusing.

 

[ascky]

Actually I think that's all drivel. If you lie on the bridge to give a greater surface area with your gold bar on top of you?

 

[Dual Op Amp]

Just jump, surely you can swim. Then, climb up the mountain to the other side.

Take off all your clothes, rip them into long threads. Tie them around one gold bar at a time, then pull them across the bridge once you're safely on the other side.

 

[Up_Creek]

Actually, if I came upon said gold bricks, and we're assuming that all this info is readily available (IE: a sign that tells me how much the bridge can handle ect) and there was a way of knowing exactly what my weight is, i'd be suspicous.
1.) Why would someone leave gold bricks infront of the bridge?
2.) Why are the bridge's tolerances only 1 kg over my weight?
3.) GOld bricks, seemingly in the middle of nowhere, and I'm the only one around

I've got to believe someone's watching me. It's just too like a trap or something. Why am I wandering the barren canyon-lands anyway? Surely not on a quest for gold. Enlightenment perhaps? A classic example of foregoing the rewards to continue on my way. I bet Buddah would know the answer to this... ;)

And since this bridge is a bridge over 'troubled' water, I'm assuming I can't swim for it (alas, I can't even swim). Perhaps the bridge is metaphorical. Like the song. The gold represents the trappings of narcotics. The point is to not take the gold across and you'll be better off, hence leaving the drug problem, the troubled waters, and if you're lucky, Simon and Garfunkel, behind me.

Do I win?

Jordan Veale

 

[Dual Op Amp]

Cut off your arm, then carry the gold bars. Go back, pick up your arm. Then, with your new found wealth, have your arm sewn back on.
Then, buy a BIG house and a Jaguar XJR!


Real Answer:
The rope is what is taking all of the tension, it's taking the weight. Take off every other step, so that the weight is cut in half. Then, grab the bars, and carefully walk across the bridge.

 

[BobG]

Actually a similar problem had one tie rope to the load, lower the bars to the bottom of chasm (assuming rope long enough to reach down to bottom of chasm, but not long enough to reach across the bridge), cross bridge (hopefully with less than 2 kgs of rope) and pull load up other side.

I think you're talking about getting 3 balls across a river on a boat. There's a possible solution depending on the density of the balls. The density would have to be less than 3 to reduce the force on the boat enough to get them across.

For this problem, we're given the fact that they're gold bars. The density of gold is around 19 (pure) to 16 (fairly impure). Tribdog's is the simplest solution.

A really big helium balloon would also solve the problem. The advantage of this solution is you could inhale the helium and talk to yourself in funny voices after crossing the bridge.

 

[Moonbear]

What the question doesn't tell you is there were originally 4 bars of gold, but the original owner didn't know much about physics, and he and his gold bar are down in the river somewhere.

Wait, Dual Op Amp's answer leaves me wondering just what part of the bridge can't support weight above 80 kg. Is it that the supports are weak, or the boards? Where's the weakest point that's going to fail if I step on with too much weight? Maybe it's just one anchor point, on the side I'm on, where the rope is starting to fray. So, I take my gold bars, grab one of the ropes, hang on tight, and when the anchor fails, I swing to the other side, then climb up the planks like a ladder. Um, assuming this is a rope bridge we're talking about. (I'm getting an image of Wile E Coyote slamming into the side of a cliff at the moment...ouch!). Though, that's how Indiana Jones would do it.

But if it's just weak planks across the bridge, you could walk along the railings, or climb under or up (depending on the structure) and hang from the supports (this approach probably works best if you're a trapeze artist).

Oh, oh, oh, I just thought of another answer. If the bridge is there, then it must have been possible to get to the other side before the bridge was built, otherwise it couldn't have been built. So, just find the long way around the bridge builders used. Erm...you might have to recruit some beavers to build a dam to make the river passable.

 

[Gokul43201]

psst BobG, there was no mention of a river anywhere in the question. I think Astronuc was lowing the bars down to the conyon floor (or riverbed, if need be).

 

[ceptimus]

These 'maximum bridge load' warning signs always have a safety factor built in, and you can be sure it's at least 10%.

So I'd just pick up the gold and tip toe over. If I was confident in my 10% safety margin, I could even take all three bars at once, and I might do that, depending on how long the bridge is, and whether or not there are any shady characters about who might steal *my* gold.

 

[Dual Op Amp]

Well, it said bridge over troubled waters, so it's assumed there is a river. But, it's the rope that takes all of the weight.The object that is anchored to each side of the canyon is the one that takes the tension. So, the only thing that the steps are doing is just adding weight.

 

[BobG]

Yeah, I had to go back to make sure I read it right.

Canyon? Bridge over troubled waters? What body of water would you expect to find at the bottom of a canyon?

At least you'd better hope so. Otherwise you'll be in for a pretty big surprise when you jump off the cliff into the canyon.

 

[Gokul43201]

Guess I forgot about the troublesome waters. You can have a canyon where the river's run dry, can't you ?

<holding blow-torch to the Colorado>

 

[FutureVeterinarian]

This is my first post, so, go with me here. Walk across the bridge, and pray while you're walking! If you remove you're shoes, and anyother item causing weight, maybe you can make it. Or, you can call a helicopter using a phone, and pay the helicopter man with you're new found wealth!
Nah... here's what I think the real anwser is. It's in white, so, highlight it.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If there is a bridge, there is obviously civilization on both sides of the bridge, otherwise, what's the bridge there for? So, if there is civilization of both sides of the bridge, go back to a city on your side of the bridge, and ask someone lighter than you to carry the gold across the bridge in exchange for one of the gold bars. It's worth it, right?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So, what do you think? Do you think it could work? :shy:

 

[bjr_jyd15]

Future Vet, I'm almost sure that the civilization would eat you alive. They'd take every one of your gold bars and teach you and everyone else in florida how to vote. ;)

 

[Bartholomew]

It says you can't THROW the gold bars across, but it never says you can't KICK them. Or make a primitive sling out of your shoelaces. Or you could use a rock to hammer the bars into frisbees... no wait, that counts as "throwing."

 

[Dual Op Amp]

Future Vet, I'm almost sure that the civilization would eat you alive. They'd take every one of your gold bars and teach you and everyone else in florida how to vote. ;)

I agree, and if that doesn't work out, you could always recount.

 

[DaveC426913]

So, can we have a hint?

 

[DaveC426913]

"...without falling through the bridge..."

Just noticed this in the original question.

The whole bridge won't collapse into the canyon, just the part you're standing on. That allows for many of the solutions mentioned already.

 

[tribdog]

Actually, it's hard to find gold bars even 1 kg. Most that are commonly available are far smaller than that. Which means you're hallucinating the whole thing, the bridge doesn't really exist, and if you try to cross it, you're going to fall into the gaping chasm.

I missed this one the first time through. I used to work at a gold mine (Battle Mountain Gold Company) and got to hold one of the big bars