Benjamin Wood
Math 007
Professor Winkler
17 April 2013
Pigeons in the Trailer
As a child, I went to a summer camp where I live, and one of the counselors knew that I was academically inclined and liked science. Because of this, he would give me riddles and simple puzzles to work on throughout the day. Among his puzzles was the “Two Hundred Pigeons” puzzle, as it is called in The Colossal Book of Short Puzzles and Problems by Martin Gardner. The entry in Gardener’s book reads:
An old story concerns a truck driver who stopped his panel truck just short of a small, shaky-looking bridge, got out, and began beating his palms against the sides of the large compartment that formed the back of the truck. A farmer standing at the side of the road asked him why he was doing this.
“I’m carrying 200 pigeons in this truck,” explained the driver. “That’s quite a lot of weight. My pounding will frighten the birds and they’ll start flying around inside. That will lighten the load considerably. I don’t like the looks of this bridge. I want to keep those pigeons in the air until I get across.”
Assuming that the truck’s compartment is airtight, can anything be said for the driver’s reasoning?
The answer, of course, is decidedly no. Because these birds are in an airtight container, the flapping of their wings simply pushes down on the truck bed with the same force as if it was their bodies resting on the bed via gravity. This comes down to simple physics, which is the section of the book this problem is in (chapter 17, problem 1). For years until I was at least 10, and probably even older, I did not understand how this problem worked. If birds are in the air, how could they add any weight? I don’t feel heavier when a bird is flying above me. It took many explanations from my father for me to finally understand the idea of force and how it all worked. I think that my biggest problem was that I always imagined that the air would disperse the force and diminish it, but this was not the case, because for each action there is an equal and opposite reaction. A simpler version of this problem is just “will the truck be lighter if the birds are flying around, or will it remain the same?”
A fault with this puzzle, to some degree, is the wording and necessity of parameters in this problem. The word “airtight” causes problems, because if the truck were truly airtight, the birds would simply be dead, and the problem would be mute. Banging on the truck would be as banging on a big coffin, the birds would not fly regardless of what you did. Additionally, because this is a puzzle, people will be paying attention to little details like this wording issue. Unfortunately, this matter of semantics cannot just be left out, because the principle upon which the solution relies requires that the truck is airtight. If there was an opening, then force could be released through there. For this reason, I’ve spent a while thinking of ways around this problem. The only true way to fix wording paradox is to alter the puzzle significantly to the point where the punch line of the question becomes:
The airtight truck is full of automated helicopters that can be turned on remotely. If they are turned on, will the truck be lighter, or unchanged?
The problem with this new wording is that the puzzle itself feels “sneakier” as it were, more conniving. In its first form, as seen above, it seems innocent and simply a farm myth that could go either way.
This myth is my favorite from the Martin Gardner book because it is so simple but all at once engages the mind in the world of physics and forces that you cannot see. As a young child, it made me want to understand what was going on and why the answer was no. I learned about Newton’s third law (and the other ones as well of course) on my own for this reason. The power to inspire someone is impressive, and for this reason I love this puzzle. There is a flaw here, though. The reason I was so enthused was that I did not know Newton’s laws, and I wasn’t able to fully think out the situation in my head when I was that young. I fear that to someone who is educated and at my age now, it is a rather simple and unimpressive puzzle, almost to the point of just being “so what?”
Because of this, I have tried to come up with a few ways of making this puzzle more difficult. One was is via omission. If the question were phrased simply: A man hauling a trailer of live pigeons bangs on the side of the trailer to lighten the load. Is his method effective? This makes assumptions including that the birds can fly, that the trailer is “air tight,” and that the birds somehow remain alive. A few other ways of making this more challenging become more math-intensive without a simple elegant solution as far as I can tell. For me, the only ways of making this problem more difficult is to add in holes in the trailer, and then question the effect that these holes would have. For example, what would the effect of a one-square-inch hole be in the top versus a 2-foot by 2-foot square in the top of the trailer? Would either of these lighten the load? Another possible way of making this more challenging is the location of the puzzle. Without getting into airflow physics, I think a simple conceptual addition would be to add a hole in the side versus one in the back of the trailer. From common experience, we know that when a truck (or any vehicle) goes by, there is a vacuum close behind it that pulls air with it. To me, theoretically, for this reason, a hole in the back would be far less effective at lightening the load (by adding in air flow) than a hole in the side, due to the low pressure behind the vehicle. If I were able to do more advanced physics perhaps this would be workable, however, then it would not make a very good puzzle because it would be solvable only by a select few. This puzzle to me does not seem to have as many variations as other puzzles in terms of expanding its difficulty, but time will tell. I have not found any other versions than what are stated above, disregarding small changes in phrasing and wording.