This Week's NPR Weekend Edition Sunday Puzzle

[john smith]

The Current Challenge (given February 22, 2004):

A private pilot has a four-seat plane, and he's offered to take three
friends up for a flight. To do his load and fuel calculations the pilot
needs to know the combined weight of his three passengers. Now, the
three passengers are sensitive about their weight, and none of them will
let anyone else know how much he weighs. And no scale at the flying club
is big enough to weigh more than one person at a time. How does the
pilot quickly get the accurate combined weight of the three passengers?

E-mail your answer to , or send a post card to:

PUZZLE
Weekend Edition Sunday
National Public Radio
635 Massachusetts Ave., NW
Washington, DC 20001

[John Harper]

Pragmatic solution: tell them to stop being childish and just tell
me what they weigh, or else stay on the ground while I go flying
and have some fun.

Of course there are a number of mathematical solutions. Personally
I wouldn't trust my passengers to do arithmetic correctly if my life
depended on it!

John

"john smith" > wrote in message
...
> The Current Challenge (given February 22, 2004):
>
> A private pilot has a four-seat plane, and he's offered to take three
> friends up for a flight. To do his load and fuel calculations the pilot
> needs to know the combined weight of his three passengers. Now, the
> three passengers are sensitive about their weight, and none of them will
> let anyone else know how much he weighs. And no scale at the flying club
> is big enough to weigh more than one person at a time. How does the
> pilot quickly get the accurate combined weight of the three passengers?
>
> E-mail your answer to , or send a post card to:
>
> PUZZLE
> Weekend Edition Sunday
> National Public Radio
> 635 Massachusetts Ave., NW
> Washington, DC 20001
>

[Dan Luke]

"John Harper" wrote:
> Personally I wouldn't trust my passengers to do arithmetic
> correctly if my life depended on it!

Any Angel Flight pilot could tell you horror stories.
--
Dan
C172RG at BFM
(remove pants to reply by email)

[John Theune]

john smith > wrote in news:vsw_b.21$OE4.9
@fe1.columbus.rr.com:

> The Current Challenge (given February 22, 2004):
>
> A private pilot has a four-seat plane, and he's offered to take three
> friends up for a flight. To do his load and fuel calculations the pilot
> needs to know the combined weight of his three passengers. Now, the
> three passengers are sensitive about their weight, and none of them
will
> let anyone else know how much he weighs. And no scale at the flying
club
> is big enough to weigh more than one person at a time. How does the
> pilot quickly get the accurate combined weight of the three passengers?
>
> E-mail your answer to , or send a post card to:
>
> PUZZLE
> Weekend Edition Sunday
> National Public Radio
> 635 Massachusetts Ave., NW
> Washington, DC 20001
>

He simply cancels the flight because his aircraft cannot take all 4 up at
once. The odds of 3 people being asked to go up in a plane together when
all of them are concerned about being underweight are vanishingly small.
Barring that they could go in to the room one at a time and weight then
selves and write down the weight on a piece of paper and insert it into a
slot in a lock box so no one could see the results until all 3 papers are
in the box. The pilot adds up the numbers and has his total weight and
no one know which wieght goes to which person.

[Big John]

John

1. Have each passenger pick up an unknown weight (suitcase, etc.) and
weigh with it to get a gross weight.

2. After all three are weighed that way, add these gross figures to
get a max gross weight of the group.

3. Take the 'added' weight (suitcases, etc.) each carried to get
weighed and weigh the three to get the excess weight.

4. Subtract the extra weights total from the max gross total and the
figure you get is the total passenger weight that can be used to
figure W & B.

May be a easier way but this will work and no individual will give
away his weight.

Big John


On Mon, 23 Feb 2004 23:58:19 GMT, john smith > wrote:

>The Current Challenge (given February 22, 2004):
>
>A private pilot has a four-seat plane, and he's offered to take three
>friends up for a flight. To do his load and fuel calculations the pilot
>needs to know the combined weight of his three passengers. Now, the
>three passengers are sensitive about their weight, and none of them will
>let anyone else know how much he weighs. And no scale at the flying club
>is big enough to weigh more than one person at a time. How does the
>pilot quickly get the accurate combined weight of the three passengers?
>
>E-mail your answer to , or send a post card to:
>
>PUZZLE
>Weekend Edition Sunday
>National Public Radio
>635 Massachusetts Ave., NW
>Washington, DC 20001

[John Harper]

In fact the problem is poorly formulated. The lockbox is
clearly the answer if they don't mind writing their weight
down. Or Big John's solution is quite neat. Or you could
have each passenger divide their weight into n unequal
parts and write each part down separately, giving you
3n pieces of paper which you then sum. No doubt you
could figure out how to use the Chinese Remainder Theorem
if you wanted to...

Or you could fly a 182 with half tanks - if they'll fit in
the plane, you'll be OK.

John

"John Theune" > wrote in message
1...
> john smith > wrote in news:vsw_b.21$OE4.9
> @fe1.columbus.rr.com:
>
> > The Current Challenge (given February 22, 2004):
> >
> > A private pilot has a four-seat plane, and he's offered to take three
> > friends up for a flight. To do his load and fuel calculations the pilot
> > needs to know the combined weight of his three passengers. Now, the
> > three passengers are sensitive about their weight, and none of them
> will
> > let anyone else know how much he weighs. And no scale at the flying
> club
> > is big enough to weigh more than one person at a time. How does the
> > pilot quickly get the accurate combined weight of the three passengers?
> >
> > E-mail your answer to , or send a post card to:
> >
> > PUZZLE
> > Weekend Edition Sunday
> > National Public Radio
> > 635 Massachusetts Ave., NW
> > Washington, DC 20001
> >
>
> He simply cancels the flight because his aircraft cannot take all 4 up at
> once. The odds of 3 people being asked to go up in a plane together when
> all of them are concerned about being underweight are vanishingly small.
> Barring that they could go in to the room one at a time and weight then
> selves and write down the weight on a piece of paper and insert it into a
> slot in a lock box so no one could see the results until all 3 papers are
> in the box. The pilot adds up the numbers and has his total weight and
> no one know which wieght goes to which person.

[BTIZ]

stand next to them and make an "educated guess".. guess high.. and if the
numbers don't work out.. tell them they can't fly until they prove they are
below a set weight...

ever want to be the weight guesser at the local carny?

BT

"john smith" > wrote in message
...
> The Current Challenge (given February 22, 2004):
>
> A private pilot has a four-seat plane, and he's offered to take three
> friends up for a flight. To do his load and fuel calculations the pilot
> needs to know the combined weight of his three passengers. Now, the
> three passengers are sensitive about their weight, and none of them will
> let anyone else know how much he weighs. And no scale at the flying club
> is big enough to weigh more than one person at a time. How does the
> pilot quickly get the accurate combined weight of the three passengers?
>
> E-mail your answer to , or send a post card to:
>
> PUZZLE
> Weekend Edition Sunday
> National Public Radio
> 635 Massachusetts Ave., NW
> Washington, DC 20001
>

[Ash Wyllie]

john smith opined

>The Current Challenge (given February 22, 2004):

>A private pilot has a four-seat plane, and he's offered to take three
>friends up for a flight. To do his load and fuel calculations the pilot
>needs to know the combined weight of his three passengers. Now, the
>three passengers are sensitive about their weight, and none of them will
>let anyone else know how much he weighs. And no scale at the flying club
>is big enough to weigh more than one person at a time. How does the
>pilot quickly get the accurate combined weight of the three passengers?

>E-mail your answer to , or send a post card to:

>PUZZLE
>Weekend Edition Sunday
>National Public Radio
>635 Massachusetts Ave., NW
>Washington, DC 20001


This one has beeen aroound before. What you do is whisper a random number to
person 1. He adds his weight to that number and whispers the result to person
2. He and person 3 dothe same. Person 3 tells the pilot the result of his
calculation. The pilot then subtracts the original random number and comes out
with the total of the passenger's weights.


-ash
Cthulhu for President!
Why vote for a lesser evil?

[Teacherjh]

>>
What you do is whisper a random number to
person 1. He adds his weight to that number and whispers the result to person
2. He and person 3 dothe same. Person 3 tells the pilot the result of his
calculation. The pilot then subtracts the original random number and comes out
with the total of the passenger's weights.
<<

This works as long as all passengers are good at math, and there are no
telephone errors.

The likelyhood of this is not something I want to contemplate.

Jose

--
(for Email, make the obvious changes in my address)

[john smith]

Ash Wyllie wrote:
>>A private pilot has a four-seat plane, and he's offered to take three
>>friends up for a flight. To do his load and fuel calculations the pilot
>>needs to know the combined weight of his three passengers. Now, the
>>three passengers are sensitive about their weight, and none of them will
>>let anyone else know how much he weighs. And no scale at the flying club
>>is big enough to weigh more than one person at a time. How does the
>>pilot quickly get the accurate combined weight of the three passengers?


> This one has beeen aroound before. What you do is whisper a random number to
> person 1. He adds his weight to that number and whispers the result to person
> 2. He and person 3 dothe same. Person 3 tells the pilot the result of his
> calculation. The pilot then subtracts the original random number and comes out
> with the total of the passenger's weights.

I like that!
Simple and elegant.

[G.R. Patterson III]

Teacherjh wrote:
>
> >>
> What you do is whisper a random number to
> person 1. He adds his weight to that number and whispers the result to person
> 2. He and person 3 dothe same. Person 3 tells the pilot the result of his
> calculation. The pilot then subtracts the original random number and comes out
> with the total of the passenger's weights.
> <<
>
> This works as long as all passengers are good at math, and there are no
> telephone errors.

Ok, then punch some random number into your calculator and have each passenger
add in his/her weight on that.

George Patterson
A diplomat is a person who can tell you to go to hell in such a way that
you look forward to the trip.

[Teacherjh]

>>
Ok, then punch some random number into your calculator and have each passenger
add in his/her weight on that.
<<

....and do it two or three times with different numbers to assure yourself that
nobody ELSE made errors. I've watched too many people do math and science,
with and without calculators, to trust such results. In calculating the speed
of a baseball (starting with reasonable assumptions) I've seen a lot of
students put down "0.024121331 mph" because that's what the calculator said.

If there's a W&B to be done, it will be ME that does it. I mever nake
mistakes.

Jose

--
(for Email, make the obvious changes in my address)

[Peter Duniho]

"Teacherjh" > wrote in message
...
> If there's a W&B to be done, it will be ME that does it. I mever nake
> mistakes.

Ne either. Oh, I think I found your "n". Want to trade? :)

The funny thing about this whole problem is that it ignores the fact that
you need not the combined weights for all three passengers, but the combined
weights of two of them (sitting in the rear seat) and the weight of the
front passenger (added to your own, of course).

It's a nice "brain teaser", but it has no practical application, at least
not with the solutions given so far.

One theoretically accurate solution would be to load up the airplane, then
measure the area of the contact patches of each tire. By dividing the area
by the tire pressure (making sure the units match, of course...for example,
measuring area in square inches, and pressure in psi), you get the
distribution of the weight at each tire, which gives you not only total
aircraft weight, but also enough information to calculate a moment, to which
you can include your own weight and position (since I'm assuming the pilot
is not in the plane, but rather is the one taking measurements), and
determine the exact location of the CG.

Of course, there's no really practical way to measure the area of the
contact patch, what with it not being exactly rectangular, there being voids
where the tread has gaps, and the like. But unlike the "add 'em all up"
solution, at least this one has the potential to actually give useful
information, if only the impracticalities could be addressed.

Pete

[David Brooks]

> This one has been around before

On Car Talk, about a year ago. The question was about the mechanics in the
Last Chance Garage wanting to know their *average* wages, so there was an
additional step. Dedicated NPR listeners should have no problem with this
one.

-- David Brooks

"Ash Wyllie" > wrote in message
...
> john smith opined
>
> >The Current Challenge (given February 22, 2004):
>
> >A private pilot has a four-seat plane, and he's offered to take three
> >friends up for a flight. To do his load and fuel calculations the pilot
> >needs to know the combined weight of his three passengers. Now, the
> >three passengers are sensitive about their weight, and none of them will
> >let anyone else know how much he weighs. And no scale at the flying club
> >is big enough to weigh more than one person at a time. How does the
> >pilot quickly get the accurate combined weight of the three passengers?
>
> >E-mail your answer to , or send a post card to:
>
> >PUZZLE
> >Weekend Edition Sunday
> >National Public Radio
> >635 Massachusetts Ave., NW
> >Washington, DC 20001
>
>
> This one has beeen aroound before. What you do is whisper a random number
to
> person 1. He adds his weight to that number and whispers the result to
person
> 2. He and person 3 dothe same. Person 3 tells the pilot the result of his
> calculation. The pilot then subtracts the original random number and comes
out
> with the total of the passenger's weights.
>
>
> -ash
> Cthulhu for President!
> Why vote for a lesser evil?
>