Original posting may be found here. It has to do with how a magician with a mass of 68 kg can cross a bridge with three gold “bricks” of 1 kg apiece, with no throwing or anything else allowed.
Putting aside the fact that these so-called ‘bricks’ will in fact be about the size of 3.8-cm cubes, or for you Americans, 1-by-1-by-pi inch vaguely-brick-shaped-objects-that-are-nowhere-near-bricklike-in-size, I have two solutions:
(1) She could put the ‘bricks’ in her pocket and walk across. Every engineer automatically builds in a safety measure into his/her tolerances, so a bridge with a weight limit of ‘70 kg’, or 680-odd newtons, should be able to handle 71 kg, or 690-odd newtons, without a problem. Probably not a good idea to do this if the wind is up though.
(2) I know if I were to be carrying forty thousand bucks of gold across a bridge, I could probably put it off for a day or two and fast until my mass was down by a kilo.
Some time back the same question (with details changed) was asked in rec.puzzles. Everyone there (except the guy who asked the question) understood that the person could not cross the bridge without losing some weight, so they were proposing various outside-the-box solutions. My favorite of these was that the person should take a powerful purgative and squat by the side of the road for a while.
While a gold piece is in the air it DOES NOT add to the force (weight) exerted on the bridge. The problem is that the force needed to toss the gold (and thus exerted on the bridge) is greater than the weight of a single gold piece. The solution (maybe, I didn’t do the math) is to juggle such that two pieces are in the air at one time. As long as the force used to toss the piece is less than or equal to 2x the weight of a gold piece, we’re ok to cross.
You know what they say, there is no such thing as a free lunch. The average force required to keep three in the air is going to have to be at least the weight of the three. At some point, you’re going to have to exceed the weight of only two of them, to maintain that average–so your solution is doomed.
RM Mentock is, of course, correct. When I first saw this question, I worked through the math, just for fun, to see what the forces would be. What you have to remember, Dave, is that there is a correlation between how hard you throw and how high the gold goes.
To get two gold pieces in the air at all times means you have to either move your hand faster or throw the gold higher, both of which mean you’re increasing the acceleration of the gold piece. Since F=ma, higher acceleration equals higher force, and thus you can never figure out a strategy where the maximum force of (magician + gold being carried + force on gold from acceleration) is less than 71 kg (X gravitational acceleration). As a matter of fact, (I think) the time-averaged force is always equal to exactly 71Xg N.
Personally, I don’t think the magician can walk across the bridge even without the gold. The problem is that 68kg is
the magician’s resting weight on the bridge. As soon as he starts to walk, the forces exerted on the bridge are greater than a 70kg weight would exert. In fact, assuming that the magician is near the weight limit of the bridge, then the bridge will start to bounce with each step, so not only do you have the extra force from the step, you also have the weight of the bridge bouncing contributing to the downward force on the bridge supports.
I give the magician 4, maybe 5 steps even without the gold before he tumbles into the river.
Depending on where and when the bridge was built, there should be safety factors built into the bridge. Limit States Design gives a Live Load (moving load) factor of 1.5 plus there is a resistance factor of 0.9 used for material resistances giving a total factor of safety of 0.6 (or 1.666… depending on how you look at it) so in all probability the bridge should theoretically be able to withstand a live load of 116.667kg (1144.5 N, come on people, let’s get it right)
Of course, being based on probabilities of failure, etc., there is the slightest probability that our dear magician will find himself in the drink. But perhaps this bit of information and advice is worth 1kg of gold to him which I would gladly take off his hands and assure his safety crossing the bridge.
If the bridge is so flimsy it can only support 70kg, it can’t be a very long one. If it’s not very long, the chasm it spans can’t be very wide either–something like 6m/20 ft across. If I were the magician, I’d just throw the gold bricks across to the other side, then saunter (gently) across the bridge to the other side, pick them up, and go on my merry way.
Since a magician usually has some “rope” (cord) on him. he could use it to tie the gold. Leave it on one side, and when he’s accoss then pull it off the far ledge.
TRH and tshirts, the puzzle does say “without throwing or dragging the gold across”. I’m not convinced the powerful purgative would do the trick either. In the last issue of Time magazine, they had this bit of trivia in their Olympics coverage:
British Judo champ Debbie Allan thought she was under the weight limit, but someone had stuffed tissue paper in the machinery, causing it to underreport results. She was 14 oz. over the 115-lb. weight category. She cut off most of her hair and stepped on the scales naked, but was still just over the limit at the official weigh-in.
So losing a whole pound must be pretty hard. Maybe liposuction would do the trick?
People here analyzing the forces have mentioned that you have the force of throwing a brick into the air is more than just the weight of the brick. Being a nitpicker, I would like to point out that catching the falling brick will also result in more force.
Of course, the final answer is still the same. The average force will be 71 kg, and at times will be even greater.
Losing weight by cutting off hair won’t get you far. Unless you have very oily hair, it doesn’t weigh much because it’s dry.
Excrement is mostly water and is relatively heavy. To lose a kilogram (as required in this version of this puzzle), one would have to excrete a full liter of fluid. Whether the purgative would cause you to excrete that much, I don’t know (it’s not like I have much experience with them). Perhaps an emetic would be needed as well…
Absolutely true. If you look at catching-and-throwing as a continuous motion, you’ll note that the entire operation is a consistent acceleration of the brick upwards, with “catching” the first half (brick velocity is downwards) and “throwing” the second half (brick velocity is upwards). Since the acceleration of the brick is upwards at all times, the extra force on the magician is downwards at all times, a result which agrees with your nitpick.
If the magician begins juggling before stepping onto the bridge, and juggles in a manner to keep 2 ingots in the air at all times, and juggles the gold high enough, so that after only a few quick steps on the bridge he is across, and catches all 3 while safely on the other side, then the “system” would only recognize 1 bar and the weight would not exceed the limit, even with the force needed to get that piece in the air.
But, I believe that REALLY high juggling breaks the “no-throwing” directive.
Although, any magician worth his 68kilos in gold would almost certainly have trained doves on hand, who could certainly be made to fly the gold across the bridge while he walked…
Then there’s also the argument regarding how much weight the bridge can support over a given area. If our hero attempts to lay on his stomach and undulate across, the bridge might hold…
And of course, the length of the span… might not be as long as the man is tall…
Unfortunately, the force exerted will average out to 1kg per brick. Furthermore, there is the issue of his arms doing the juggling--they are moving up and down, also exerting force.
The peak force will be *HIGHER* while juggling the bricks than while simply carrying them.