weighing elephant

I think this is a well-known puzzle. Hundreds of years ago, a king of an Asian country who lived in a port city, received a visit from a king of adjacent country, his friend. The visitor brought a present with him. It was an elephant. The visitor gave it and said, 'Can you measure the elephant's rough weight in a day?' The king of the port city consulted with the retainers. 'We just have beam scales weighing bags. Do you have any ideas?' One vassal said, 'I can make the relevant measuring equipment assembling large levers and pulleys, your majesty.' 'Can you make it in a day?' '......I can't.' Another vassal said, 'How about weighing in pieces after killing the elephant?' 'I won't.' At last they found the method and measured the elephant's approximate weight without sophisticated devices. What was the method? (I know only one way in the original story. Maybe there are better ways.)

They let the elephant board a large empty ship in harbor. (Probably it was difficult work.) The ship sank to some degree and a sailor marked the water level on the hull. (Is it draft?) Then they let the elephant leave the ship and loaded the ship with freights until she sank to the mark on her. Finally they weighed every freight respectively and summed up.

They took the elephant down to a pool and got it to step onto a barge. The barge collapsed under the elephant's weight. The elephant was unharmed, as they are good swimmers - this is true - and can breathe through their trunks.

The level of the pool rose, and they multiplied this rise by the circumference of the pool to estimate the elephant's volume. They knew that the elephant was a bit heavier than water (as it sank, but not quickly) and so they had a rough figure for the elephant's weight, expressed in the weight of water. A cubic metre of water weighs very nealy one tonne, so they now knew the elephant's weight.

<snip>

I was under the impression that a cubic metre of water weighs exactly one tonne. Is my impression mistaken? Do you have a reference?

The weight of a cubic metre of water depends on the temperature and (less so) on the pressure. If I remember correctly, equality holds at 4 degrees C and pressure of 1 bar.

This is rec.puzzles. I didn't want to start an endless cascade of threads discussing the precise temperature and pressure necessary for a cubic metre of water to weigh exactly one tonne - nor an argument over the distinction between mass and weight - nor an argument about the problems caused by surface tension. I considered these, and the fact that they're essentially irrelevant in this context, sighed, and wrote 'very nearly one tonne.' (1)

jds

(1) Except for some reason I wrote 'very nealy'. I blame it on pressure, tension, and an excess of gravity.

True, but this is *also* Usenet...

...so you were doomed!



ObSomewhatDerivativePuzzleAndNoIDon'tKnowTheAnswer: a telephone engineer is called to a block of flats (I believe 'apartment building' is the correct translation here) in which every apartment has at least one telephone. In fact, those on floor F have ceil(F/10) telephones, for each F > 0; yes, the guy up in the penthouse has quite a few phones, some of them modems and fax machines. (Quite a few of the lines are used for data, in fact, and that is significant.) There are 100 floors, and 101 - F flats/apartments on each floor.

Room Numbers Number of phones per room 100 - 199 1 200 - 298 1 300 - 397 1 . . 1000 - 1090 1 1100 - 1189 2 1200 - 1288 2 . . 9900 - 9901 9 10000 10

For the sake of clarity in the face of international differences wrt floor numbering, you may assume that floor 0 is the floor at street level, which has no flats or apartments. But it *does* contain the 'switchboard' (which I've put in quotes in case I've misunderstood switchboards!). Each phone line terminates at a socket in a huge board. Plugged into each socket is a cable which leads to an outside phone connection. (I'll call each end 'internal' and 'external' - so the 'external' end of the wire leads to the outside world.) The phone number for each line is clearly marked on the external socket, but not on the internal socket.

Henry, the mild-mannered caretaker, is a perfect logician, which may explain why he's a caretaker. I believe the correct translation is 'janitor'. He is responsible for the cables correctly connecting the outside phone connections to the board.

Did I say 'perfect'? Almost perfect, I meant. One day, he was so engrossed in building the world's best ever pencil sharpener using only balsa wood, glue, and a bucketful of infinitely many spherical magnets, that he didn't notice his 6-year-old son wander into the phone room. (You know what's coming, yes?)

And indeed, a couple of hours later, it emerged that the little boy had messed up the board. He had randomly chosen two cables, removed the external end of one and the internal end of the other, and re-connected them like this:

BEFORE AFTER

Outside Outside

The 1991 US edition of the standard defining the International System (modern metric measure) is available online in PDF format at the URL <http://physics.nist.gov/Document/sp330.pdf>. It is quite readable and includes an appendix, longer than the document itself, detailing important changes that have been made to the system since 1901.

The original idea of the kilogram was that it would be the mass of a cubic decimeter of water, and if that was the case, then the the mass of a cubic meter would indeed be exactly 1 tonne, also called a metric ton or megagram. However, if that ever was the official standard, it was abandoned long before 1901, when it was realized that a physical standard object was more practical for several reasons. (One reason is that it does not have to be measured at a specific and exact temp- erature, whereas since the density of water varies, a water standard would have to specify a particular temperature.)

The kilogram is now defined simply as the mass of a certain object, the standard kilogram, which is located in France.

The definition of the meter has also changed. I've read that it was originally proposed to be the length of a pendulum with a period of 2 seconds, but this was quickly rejected, presumably because it was realized that the intensity of the gravitational field is not exactly uniform over the Earth's surface. The first official definition was 1/10,000,000 of the distance from the North Pole to the Equator along the meridian through Paris, which happens to be quite close to the pendulum length, but again this is quite impractical.

Three other definitions have followed over the years

... The kilogram is now defined simply as the mass of a certain object, the standard kilogram, which is located in France. ... How much does it weigh?

About 9.8N, give or take.

no) I can think of several strategies.

1) Pawn it off on his six year old son being foremost.

2) Round up a partner armed with a cell phone, and the master keys. (after giving notice, of course, alternately he may be fortonate enought to find a block of several adjacent unoccupied apartments) after a few of these he can discover the pattern, and make the rest of the swaps. Of course,if he's a competent repairman, he still has to verify each and every connection once done (groan). Which brings is back to the origial problem with a 10% chance that anyone's home at a given number. Although, on the bright side, there is a considerably greater chance that a given appartment has an answering machine.

3) after considering (2) calling the phone company is looking better all the time. It may well be the low-cost solution

Yet another point, they forgot to include the weight of the elephant's supervisors in their calculations.