# The African elephant and the fly [closed]

This is from a republishing of an old taxonomy book.

An African elephant weighs 4536 kg.

A fly weighs 64.8 mg.

What is the weight of an African elephant with a fly on his head?

• A puzzle that's intentionally worded to be misinterpreted isn't a puzzle but an exercise in mindreading. – xnor Apr 21 '15 at 9:06
• If the fly makes the elephant sneeze, it reduces the overall weight by much more than the weight of a fly. – Florian F Apr 21 '15 at 9:39
• As a note, KG is a unit of mass, typically weight is measured in newtons – Sam Apr 21 '15 at 13:40
• I second @xnor and would submit the following: xkcd.com/169 – Engineer Toast Apr 21 '15 at 14:54
• Oh, come now. It's a riddle/joke. You might not like it, but it's perfectly clear what it's asking...or if it's not, that's the point. – galdre Apr 21 '15 at 18:48

The weight is:

4536 kg. No matter what the African elephant has on his head, he will still weigh 4536 kg.

• Haha, if this is the answer i like the riddle, nice joke :) – Vincent Apr 21 '15 at 9:02
• Well, try to explain to a truck driver that the weight of his truck with an elephant above it is the same as there was nothing there. You solved every wheel transportation problem! – Narmer Apr 21 '15 at 14:18
• @Narmer I'm trying hard to imagine what problems would be solved by putting elephants above trucks, but I do like the idea. – JiK Apr 21 '15 at 14:46
• @JiK, the 'elephant transportation' problem? – A E Apr 21 '15 at 15:53

I like elephants.

It appears that the measurements were originally expressed in imperial units, with the weight of an African elephant specified as 10000 lb (about 4536 kg), and the weight of a fly as 1 grain (about 64.8 mg). The weights were later converted to kg and mg respectively (possibly by the republisher?) without the appropriate rounding considerations.

Not only is the fly's weight negligible for the calculation of the total weight, but also the last 2 or 3 digits in the African elephant's weight are, at best, insignificant.

The weight of the combination "an African elephant with a fly on his head" is 4536.0000648 kg, if it was the particular elephant and the fly that was mentioned. Given that the weight of the elephant was likely not to have been 4536.0000000 kg because that's a suspiciously round figure and far beyond the precision of measurement and likely to change as the elephant breathes, it would make sense to report the combined weight simply as 4536 kg.

The weight of the elephant that is specified as having a fly on his head is 4536 kg, if it is elephant whose weight was mentioned before..

If we take statements like "An African elephant weighs 4536 kg" to mean there's one such elephant, not as a general fact about elephants nor of a specific elephant referred to, then we can't say anything precise about the elephant and fly mentioned later. Actually it's not clear which elephant is later asked about as "an elephant". But, a reasonable estimate could come from the statistic that African elephants weigh up to 4000–7000 kg.

• I answered it first :P – user2408578 Apr 23 '15 at 8:09

The avarage height of an elephant is $4 m$, we can say that the center of mass of the elephant is roughly at $2m$ from the tip of his head. Being the fly millimiters long his center of mass can be ignored.

Since here the weight is intended in $N$, I'm going to translate it in mass ($kg$) units. Everything is calculated on earth.

We have:

Mass of the elephant on earth $= M1 = \frac{4536N}{9,8\frac{m}{s^2}} = 462,85kg$

Mass of the fly on earth $= M2 = \frac{0.0000648N}{9,8\frac{m}{s^2}}= 6,61\times 10^{-6}kg$

Distance between the centers of mass $=r=2m$

The gravitational constant $=G= 6.673×10^{−11} N\cdot(\frac{m}{kg})^2$

The gravitational pull of the fly on the elephant is given by:

$F=G\cdot\frac{M1\cdot M2}{r^2}=6.673\times10^{-11}N\cdot(\frac{m}{kg})^2\cdot\frac{462,85kg\cdot 6,61\times 10^{-6}kg}{(2m)^2}\simeq 5,1\times 10^{-14}N$

So the elephant receives a gravitational pull from the fly equal to $5,1\times 10^{-14}N$ which is opposite to the earth gravitational pull. Now the elephant weighs:

$4536N-5,1\times 10^{-14}N=4535,99999999999949N$

Still not the same!

It will be

Weight of African elephant + weight of fly which are under test for weight

because the one which you mentioned may not be under test for weight. :) you mentioned An African elephant weighs 4536 kg.

The one which is tested may weigh 4500 kg or anything that is in the possible range for an African elephant's weight.

The elephant with a fly on its head will weigh actually a bit less than without the fly!

The fly will exert an upwards gravitational force to the elephant, thus countering part of the force by Earth. If we interpret the definition in Wikipedia ("the weight of an object is usually taken to be the force on the object due to gravity") in a suitable way, it means the weight of the elephant is decreased by the fly.

• No, see Narmer's answer. if that'd be true I could fly if i held a 70kg sack of potato's on my head, or an elephant but then i'd be launched, I like to fly safe ;) – Vincent Apr 22 '15 at 11:38
• @VincentAdvocaat I don't see why you should be able to fly. The effect of the sack of potatoes would be extremely small, and in addition, you would have to carry the weight of the potatoes along with you which would more than cancel the effect of the sack on your weight. – JiK Apr 22 '15 at 11:51

The elephant will weigh 4536000064.8 mg.

• buzzer Wrong! – Scruffy Apr 21 '15 at 9:48
• luking at the fly, as the fly mentioned during weigh measure and the latter fly are different what if the latter fly was pregnant at the time it sat on the elephant's head?. there is no unique answer for this puzzle !!!! :( or is it? – divine Apr 21 '15 at 10:24