Questionable puzzle from a book

[spockjones20]

I came across this puzzle in the book The Big Book of Riddles Puzzles and Enigmas and I am also certain I have seen it elsewhere throughout the internet. The puzzle as written goes like this

"A troubadour holding three objects (a ball, a hat, and a bowling pin) arrives at a bridge. The bridgekeeper warns him, 'The bridge won't bear more than your weight plus a maximum of two objects, and its not possible to throw the objects to the far side.' The troubadour nevertheless manages to get to the other side carrying his three objects in a single crossing. How does he do it?"

Now, this being a puzzle forum, I will first give you the pleasure of solving this, just in case you have a burning desire to do so, and then I will post why I believe this to be questionable.

 

[Evo]

I came across this puzzle in the book The Big Book of Riddles Puzzles and Enigmas and I am also certain I have seen it elsewhere throughout the internet. The puzzle as written goes like this

"A troubadour holding three objects (a ball, a hat, and a bowling pin) arrives at a bridge. The bridgekeeper warns him, 'The bridge won't bear more than your weight plus a maximum of two objects, and its not possible to throw the objects to the far side.' The troubadour nevertheless manages to get to the other side carrying his three objects in a single crossing. How does he do it?"

Now, this being a puzzle forum, I will first give you the pleasure of solving this, just in case you have a burning desire to do so, and then I will post why I believe this to be questionable.

He juggled the objects as he walked across, that way at least one object was always in the air.

 

[QuarkCharmer]

Couldn't he just put the hat on?

Otherwise, he must have been a naked troubadour.

 

[spockjones20]

Correct! Now to my question. Wouldn't the downward acceleration of the object in the air create the same amount of force as holding the additional object in his hand, causing the bridge to break in either case?

 

[QuarkCharmer]

Correct! Now to my question. Wouldn't the downward acceleration of the object in the air create the same amount of force as holding the additional object in his hand, causing the bridge to break in either case?

Yup.

 

[Evo]

Correct! Now to my question. Wouldn't the downward acceleration of the object in the air create the same amount of force as holding the additional object in his hand, causing the bridge to break in either case?

Not necessarily. For example if the bowling pin is in the air when the hat comes down. By choosing the order of juggling, it won't be an issue.

My problem with the puzzle is that it's ridiculous. He has a hat, a ball, and a bowling pin. We can assume the hat is light, the ball may be hollow and also light, but we don't know. But the guy says "any two objects, which leads us to assume that the bridge can handle the weight of the two heaviest objects at once. I would assume that the troubador is juggling all three items with one hand, so two objects are in the air at all times.

 

[D H]

Correct! Now to my question. Wouldn't the downward acceleration of the object in the air create the same amount of force as holding the additional object in his hand, causing the bridge to break in either case?

On average, yes. Instantaneously, no. Juggling would make those instantaneous forces much larger than they would be by simply carrying the objects across the bridge.

This is one of those stupid riddles invented by people who don't know physics.

 

[spockjones20]

Evo - My favorite part is how he knows what his weight is as soon as he reaches the bridge.

Part of me wishes I was not into physics and could just enjoy puzzles like this at face value. As they say, ignorance is bliss! Then again, knowledge is power!

 

[Jimmy Snyder]

As do all forces, the force used to accelerate the juggled objects requires an equal and opposite force. This force must be supplied by the bridge.

 

[D H]

Not necessarily. For example if the bowling pin is in the air when the hat comes down. By choosing the order of juggling, it won't be an issue.

Yes, necessarily. The average force will be the same as if the objects were walked across, and per the riddle, that is more force than the bridge can bear. Juggling won't help matters one iota. It will instead exacerbate the problem.

My problem with the puzzle is that it's ridiculous. He has a hat, a ball, and a bowling pin. We can assume the hat is light, the ball may be hollow and also light, but we don't know. But the guy says "any two objects, which leads us to assume that the bridge can handle the weight of the two heaviest objects at once. I would assume that the troubador is juggling all three items with one hand, so two objects are in the air at all times.

The first time I came across this riddle it was three balls, or three bowling pins. Perhaps the riddle was modified because some non-lateral thinking physicist said that the answer was wrong. Or perhaps the riddle was modified to make it more colorful. In any case, juggling is not the answer.

 

[D H]

As do all forces, the force used to accelerate the juggled objects requires an equal and opposite force. This force must be supplied by the bridge.

Hey! What's your real name and what did you do with the real Jimmy Snyder? This answer is completely devoid of humor. There has to be a good joke lurking about somewhere in this puzzle.

 

[Evo]

Yes, necessarily. The average force will be the same as if the objects were walked across, and per the riddle, that is more force than the bridge can bear. Juggling won't help matters one iota. It will instead exacerbate the problem.



The first time I came across this riddle it was three balls, or three bowling pins. Perhaps the riddle was modified because some non-lateral thinking physicist said that the answer was wrong. Or perhaps the riddle was modified to make it more colorful. In any case, juggling is not the answer.

If two objects are in the air at all times, how would the downward force of one object exceed the weight of the two heaviest objects? I'm sure you're right, but with one hand juggling, I think it's possible. I just put on my coffee, so maybe I won't think that after a pot.



Edit: LOL! I just read a discussion of this scenario on the mythbusters page (they were using three identical bowling balls) and it went from no, to well if it's one handed, to no, to ok, it's possible under certain circumstances, to "An interesting point to note is that given how weak the bridge is, the force of the juggler walking on it would likely break it as well."

So I retract my answer and defer to those more knowledgeable.

 

[Jimmy Snyder]

Rather than allow this myth to go on forever, why don't the Mythbusters just get a juggler and an accurate scale and put this thing to rest?

 

[D H]

If two objects are in the air at all times, how would the downward force of one object exceed the weight of the two heaviest objects? I'm sure you're right, but with one hand juggling, I think it's possible. I just put on my coffee, so maybe I won't think that after a pot.

It doesn't matter how you are juggling. The answer is the same: Juggling won't work.

Let me qualify what I mean by juggling. Tossing one of the objects high up into the air, dashing across the bridge with two objects in hand, and finally catching the tossed object on the other side of the bridge isn't juggling. By juggling I mean (and the standard answer to the riddle) means that each object is tossed into the air a many times while crossing the bridge.

One way to look at it is that the average height of the juggled objects doesn't change from one juggling cycle to the next. The time-averaged force over one juggling cycle needed to keep the objects at that average height is thus the total weight of the juggled objects.

Another way to look at it is start with one juggled object. When the juggled object is in flight the weight (downward force) of the juggler+juggled object is just that of the juggler. When juggler catches the object, he must exert a force on the object equal to the object's weight plus an additional force to change its momentum from downward to upward. The weight of juggler+juggled object will be the weight of the juggler plus the weight of the object plus this additional force needed to reverse the object's momentum. Plotting this force over time will result in a curve that is flatlined at the juggler's weight for some time, then briefly increase to well over the sum of the weights of the juggler and juggled object. The average force is the weight of the juggler plus the juggled object. Now put three objects in motion and that flatline part of the curve is no longer flat. The force is more or less sinusoidal, centered on the combined weights of the juggler+juggled objects.

The peak force is much greater than the combined weights of the juggler+juggled objects. The net result would be equivalent to marching (with very heavy steps) across the bridge.

Marching can be quite deleterious to bridges.