To continue with the Monty Python quotes… “No poof-tahs!”
While this is an old thread, I couldn’t resist. Why doesn’t he just cross the bridge in two trips and temporarily bury the gold pieces he can’t carry? I also like the stripping suggestions. That magician’s cape alone has got to weigh a ton. Alternatively, he could take a large helium balloon to help take off some pounds.
A magician must cross a bridge carrying three gold pieces.
I’ll prefacing this by saying that I am pretty stupid. Cecil says that the magician couldn’t use the juggling method because his average weight would be more than 70 kg. If one piece is always in the air, at what point does he weigh more than 70 kg? I realize that to throw the gold into the air a downward force would be exerted on him that would be more than just the 1kg of the gold, but I thought that that would just be one at a time and would go away by the time he threw the next piece. Are two pieces in the air at once or just one? Please help fight my ignorance, thanks.
ETA - Is the downward force answer the one that he was going for? If so I get it, but it seems like he was going for a different answer.
The typical juggling pattern has two objects in the air at a time. One throw and one catch are near simultaneous, though, so there might be two objects in hand simultaneously.
But in order to get the 1kg of gold moving in a trajectory through the air, he is going to have to excert more force than holding that 1 kg stationary. The loading is going to be cyclical, with higher peaks and lower valleys, but the average force to get the three pieces across in one trip will be 68 + 3.
Now if one of the pieces of gold were a bird with wings, then it could impart lift via wings. That lift could be distributed on the air, which might spread out and leak around the sides of the bridge. But then, if the gold had wings, he could fly it over the river/chasm off to the side of the bridge so it isn’t directly over the bridge. Therefore the upward lift by the air is not countered by downward force on bridge, but downward force on river/chasm.
As for the wording of the puzzle, the question proposed that he is a magician. That word is ambiguous, but the solution appears to be using the word in the sense of a performer rather than the sense of a spell-caster. Ergo, the presumption is that a magician is going to be an experienced juggler. I’m not sure that’s a valid assumption. Why is he a magician, and not a circus clown? They’d be more likely to know how to juggle, IMO. (Because a circus clown is not likely to have 3kg of gold?)
If I were faced with the dilemma, I’d be concerned the way FordPrefect is and take a different route. Hell, I’d avoid bridges where the structural rating is within 2 kg of my mass, barring emergencies.
So the downward force angle is the answer he was going for? Ok, that makes sense, I get that, thank you. For some reason it just seemed like he was going for something else.
Thanks.
Hmm. What if the magician were to tie the gold pieces to his staff/wand with string, kind of like a bolas arrangement, and then spin the staff. The centrifugal force would send the gold pieces outward. And the twisting motion should have no up/down component.
Might this work?
Maybe he should exchange the gold for certificates. 
I know, that’s not in the rules. Just kidding. But I still like the helium idea.
The horizontal forces on the gold are independent of the vertical forces on them. He’d still need to be exerting the same upward force on them to support them, and hence they’d still be exerting the same downward force on him (and indirectly, on the bridge).
He could form the gold into a Whirly-gig, and spin it to provide enough downward force to make up the 1 kg overage.
A downward force would increase the load on the bridge, not decrease it.
Powers &8^]
There are only 2 options:
- A hydrogen balloon (due to the worldwide shortage of helium).
or
- Chop off one arm, store in ice. Retrieve later for surgical attachment.
When I saw the title, my first thought was that it was a variation of “2+2=5” (e.g. 2.48+2.48=4.96; if rounded but still added as if before rounding, this becomes 2+2=5; for the current problem, use 0.666… for 1 and you get 68 + (3 x 0.666…) = 70), but apparently not. The hydrogen/helium balloon idea sounds like the best suggestion, nothing about the riddle says it isn’t allowed. Or, does he have to go to the bathroom? It is possible to lose 1 kg that way (urine and feces). And/or just wait around until he feels thirsty and he could easily take off 1-2% of body weight without becoming dangerously dehydrated.
The downward force will be dispersed through the air. If the bridge is relatively open (I imagined a rope bridge with wooden slats, but I see that’s not specified in the column), or if the whirly-gig is held near or over the edge of the bridge, most of the force won’t be felt by the bridge.
It certainly will not, no way, no how, increase the total force on the bridge, since all the downward force (and then some) is balanced by upward force on the whirly-gig.
Sometimes a swallow is worth its weight in gold.
It will only be balanced (I assume you’re referencing Newton’s Third Law) if the bridge doesn’t collapse, which it will because the whirlygig is pushing down on it.
I mean, you couldn’t send an elephant across and say that its not exerting a downward force on the bridge just because Newton’s Third Law says there is an equivalent upward force on the elephant.
Powers &8^]
A whirly gig is putting a force onto the air directly, similarly to a flying bird. The air is then pushed down, putting a force on whatever is below it.
If you can swing the whirly gig over the edge of the bridge such that some of the force from the air is on the bridge, then potentially you can relieve some of the weight the bridge is carrying.
But I wouldn’t trust my life to hoping that worked.
I wouldn’t trust the bridge with my life period, gold or not, because if it were really that close to failure, it could go at any time while you were walking across it (plus, just taking steps creates forces that are higher; you’d have to slowly shuffle across being sure to keep your weight balanced).
If he has a rope of sufficient length, he can just string it up so that it’ll enter the bridge as he exits it. Assuming there are no bandits that’ll pounce and cut the rope, taking the gold.
Agreed and already stated in post 25.
Hell, I’d be worried there are bandits that will pounce and take the gold off my carcass, after ensuring that I am a carcass.