The problem is one of seeing things differently depending on the arrangement
of things. The question was, basically, how can you take four pennies, line
them up in two straight lines, with three pennies in each line.
The other similar problems in the homework were simple (remove one
matchstick from the arrangement of four squares and leave three squares,
etc.). This one left me bewitched, bothered, and bewildered. And
bedraggled.
What am I missing? (Besides a cerebral cortex?)
Jim Beaver
I think what you missed is that the person who wrote the question
thinks that a straight line of three pennies can be formed from a
stack of two pennies and a separate "stack" of one penny.

Mark Brader, Toronto  "Jargon leakage is getting to be a real problem;
m...@vex.net  sb should do sth about it." R.H. Draney
Tshape.
?? If the top bar of the T has three pennies, the vertical bar will
only have two, won't it?

Cheers,
Harvey
Perhaps you have to consider one pile of two pennies plus one pile of
one penny to be a straight line.
21




1
There's also a spherical geometry solution if you consider a geodesic to
be a straight line: One penny at the North Pole, one at the South Pole
and the other two anywhere else, say London and Moscow. The zero
meridian goes through the NPole, London, and SPole. The 37th meridian
goes through NPole, Moscow, SPole.

Mike Williams
Gentleman of Leisure
In addition to the suggestions here, I suppose one could also say
pedantically that a line of four pennies contains in it two lines of
three pennies (the three on the right end of the line and the three on
the left end of the line). Even more pedantically, it contains four
lines of three pennies (remove any one penny leaves three pennies in a
line, although maybe not all touching).

Mark Thornquist
Do let us know next week what the "official school answer" is.
The solutions presented so far seem a little advanced for second grade work.
Jeff

Jeffry Wisnia
(W1BSV + Brass Rat '57 EE)
The speed of light is 1.8*10^12 furlongs per fortnight.
I think I see the following problem:
There are three pennies in line A
There are three pennies in line B
In order for there to be only four pennies total, that would mean that
two pennies are in both line A and line B. Call those pennies 1 and 2.
If pennies 1 and 2 are in different places, then lines A and B intersect
at *two different locations*. In Euclidian geometery, that doesn't happen.
But pennies 1 and 2 cannot be in the same location, because they are solid
objects. Even if you put one on top of the other, one will be higher and
your two lines won't actually cross in 3D space. If the teacher had said
"four dots" or "four X's", you could have a solutiononly if you allowed
two of the dots or X's to overlap, like this:
1&2 . . 3
4 .

Please reply to:  "One of the hardest parts of my job is to
pciszek at panix dot com  connect Iraq to the War on Terror."
Autoreply is disabled   G. W. Bush, 9/7/2006
First answer wins the prize (despite the "cheat" of stacked pennies being
considered to form a straight line in 3D space). The teacher filled me in
on it this afternoon and tried to convince me not to be embarrassed at not
being smarter than a second grader.
Jim Beaver
I would have asked that teacher whether she thought that problem/answer
up herself or if it can be found in a published schoolbook. <G>
> Do let us know next week what the "official school answer" is.
> The solutions presented so far seem a little advanced for second grade work.
I think so too. Here is a whole page of matchstick puzzles:
www.learningtree.org.uk/stickpuzzles/stick_puzzles.htm
Les
In that case, (P is a penny,  shows a straight line):

P P P P


charles
> There's also a spherical geometry solution if you consider a
> geodesic
> to be a straight line: One penny at the North Pole, one at the
> South
> Pole and the other two anywhere else, say London and Moscow. The
> zero
> meridian goes through the NPole, London, and SPole. The 37th
> meridian goes through NPole, Moscow, SPole.
I like this answer a lot better.
The "stack" answer isn't two straight lines by any apparent
commonsense notion of "straight".
The geodesic example does work  e.g. great circle routes are
"straight" from this perspective.
Wait a minute.
If we are going to say that a stacked arrangement works because the
pennies are in a straight line from above (ABD) or below (ACD):
B
A C D (viewed from the side)
Then we can arrange the pennies in a square, viewed from the top as
A B
C D
because the pennies are in a straight line ABD when viewed from the
upper right side, and in a straight line ACD when viewed from the
lower left side.
But it's an unusual definition of a "straight line" to say the line
only has to be straight when viewed from a certain angle.
*We* aren't. The *teacher* is.

Mark Brader  I rise to speak ... well, actually, I don't rise,
Toronto  nor do I speak, but I lounge to type in his defense.
m...@vex.net   Bob Lipton
>There's also a spherical geometry solution if you consider a geodesic to
>be a straight line: One penny at the North Pole, one at the South Pole
>and the other two anywhere else, say London and Moscow. The zero
>meridian goes through the NPole, London, and SPole. The 37th meridian
>goes through NPole, Moscow, SPole.
I love AFCA. Jim's gotta print this out and take it to the second
grade teacher.
What kind of arrangement did you make for Vancouver education? I
missed the conclusion of that discussion.

Tomorrow is today already.
Greg Goss, 19890127
Count again.
I realized that transplanting my daughter to Vancouver to sit with a
stranger (babysitter) and another stranger (teacher) for six months while I
worked 6 a.m. to 10 p.m. five days a week was going to do neither of us any
good. And she expressed severe homesickness for her friends and her nanny
after only two days away. I decided to leave her in school in L.A. with her
nanny and come home as often as I could. Flew home this weekend for
Halloween and am having a wonderful time.
Jim Beaver
Did you ask the teacher what it was supposed to teach?
Right angles. Oh hang on, that doesn't work either... I dunno! If it
was five it would be easy  are you sure it wasn't a typo?
There's nothing in the problem, as posed, that says that you cannot
provide another penny.
> The question was, basically, how can you take four pennies, line
> them up in two straight lines, with three pennies in each line.
> ...
> What am I missing? (Besides a cerebral cortex?)
Is this the answer?
1 2 3
O O O O
1 2 3
Les
> Kajikit <kaj...@jagcon.com> wrote:
>> On Fri, 31 Oct 2008 13:05:56 0700, "Jim Beaver"
>> <jumb...@prodigy.spam> wrote:
>>
>>> My kid is in second grade. She brought home a homework problem that stumped
>>> her. It stumped me, too. I did not think I was stupid, but now I wonder.
>>>
>>> The problem is one of seeing things differently depending on the arrangement
>>> of things. The question was, basically, how can you take four pennies, line
>>> them up in two straight lines, with three pennies in each line.
>>>
>>> The other similar problems in the homework were simple (remove one
>>> matchstick from the arrangement of four squares and leave three squares,
>>> etc.). This one left me bewitched, bothered, and bewildered. And
>>> bedraggled.
>>>
>>> What am I missing? (Besides a cerebral cortex?)
>>
>> Right angles. Oh hang on, that doesn't work either... I dunno! If it
>> was five it would be easy  are you sure it wasn't a typo?
>
> There's nothing in the problem, as posed, that says that you cannot
> provide another penny.
Kobiashi Maru!

"I have never yet encountered a semitrailer in my bathroom." Jen puts a
bright face on the state of the transit system in AFCA.
I like either the two collinear lines, or the two geodesics answers
best. If the teacher is trying to encourage "outofthebox"
thinking, then ...
Les Albert <lalb...@aol.com> wrote:
> 1 2 3
>O O O O
>1 2 3
... is the best answer. (Les wasn't first with it, but drew it best.)
> On Oct 31, 1:05 pm, "Jim Beaver" <jumble...@prodigy.spam> wrote:
> > My kid is in second grade. She brought home a homework problem that stumped
> > her. It stumped me, too. I did not think I was stupid, but now I wonder.
> >
> > The problem is one of seeing things differently depending on the arrangement
> > of things. The question was, basically, how can you take four pennies, line
> > them up in two straight lines, with three pennies in each line.
> >
> > The other similar problems in the homework were simple (remove one
> > matchstick from the arrangement of four squares and leave three squares,
> > etc.). This one left me bewitched, bothered, and bewildered. And
> > bedraggled.
> >
> > What am I missing? (Besides a cerebral cortex?)
> >
> > Jim Beaver
>
> In addition to the suggestions here, I suppose one could also say
> pedantically that a line of four pennies contains in it two lines of
> three pennies (the three on the right end of the line and the three on
> the left end of the line).
That was my thought, too. And since this is Grade 2, it shouldn't get
any more complicated than that. It seems like a good way to encourage
outsidethebox thinking at that age.
> Even more pedantically, it contains four
> lines of three pennies (remove any one penny leaves three pennies in a
> line, although maybe not all touching).
>
The weakness there is that except when all four are lined up, only one
line of three exists at one time. The problem asks for two.

bill
remove my country for email
"How to embarrass your parents".
>> In addition to the suggestions here, I suppose one could also say
>> pedantically that a line of four pennies contains in it two lines of
>> three pennies (the three on the right end of the line and the three on
>> the left end of the line).
>
> That was my thought, too. And since this is Grade 2, it shouldn't get
> any more complicated than that. It seems like a good way to encourage
> outsidethebox thinking at that age.
>
>> Even more pedantically, it contains four lines of three pennies
>> (remove any one penny leaves three pennies in a line, although maybe
>> not all touching).
>>
> The weakness there is that except when all four are lined up, only one
> line of three exists at one time. The problem asks for two.
If the context is "line segments"  and I've no idea if 2nd graders are
exposed to line segments  4 points in a line define 6 line segments
between any set of 4 or fewer points: 1 line segment of 4 points, 2 of 3
points and 3 of 2 points.
>On Sat, 1 Nov 2008, Jerry Bauer wrote:
>
>> Kajikit <kaj...@jagcon.com> wrote:
>>> On Fri, 31 Oct 2008 13:05:56 0700, "Jim Beaver"
>>> <jumb...@prodigy.spam> wrote:
>>>
>>>> My kid is in second grade. She brought home a homework problem that stumped
>>>> her. It stumped me, too. I did not think I was stupid, but now I wonder.
>>>>
>>>> The problem is one of seeing things differently depending on the arrangement
>>>> of things. The question was, basically, how can you take four pennies, line
>>>> them up in two straight lines, with three pennies in each line.
>>>>
>>>> The other similar problems in the homework were simple (remove one
>>>> matchstick from the arrangement of four squares and leave three squares,
>>>> etc.). This one left me bewitched, bothered, and bewildered. And
>>>> bedraggled.
>>>>
>>>> What am I missing? (Besides a cerebral cortex?)
>>>
>>> Right angles. Oh hang on, that doesn't work either... I dunno! If it
>>> was five it would be easy  are you sure it wasn't a typo?
>>
>> There's nothing in the problem, as posed, that says that you cannot
>> provide another penny.
>
>Kobiashi Maru!
Gesundheit!

Peter
I'm an alien
email: home at peteward dot gotadsl dot co dot uk
Death is too permanent for my tastes.
 Groo
Thank God for that "No Parent Left Behind" program.

M C Hamster "Big Wheel Keep on Turning"  Creedence Clearwater Revival
>Jim Beaver wrote:
>> My kid is in second grade. She brought home a homework problem that
>> stumped her. It stumped me, too. I did not think I was stupid, but now
>> I wonder.
>>
>> The problem is one of seeing things differently depending on the
>> arrangement of things. The question was, basically, how can you take
>> four pennies, line them up in two straight lines, with three pennies in
>> each line.
>>
>> The other similar problems in the homework were simple (remove one
>> matchstick from the arrangement of four squares and leave three squares,
>> etc.). This one left me bewitched, bothered, and bewildered. And
>> bedraggled.
>>
>> What am I missing? (Besides a cerebral cortex?)
>>
>> Jim Beaver
>
>
>Do let us know next week what the "official school answer" is.
>
>The solutions presented so far seem a little advanced for second grade work.
>
We never got an answer to that drawing that Lesmond posted, either.
That continues to haunt me.
That's absolutely right.
So the answer is
0
0 0 0
0
which indeed consists of four pennies (plus another penny) lined up in
two straight lines, with three pennies in each line.
I think we will were still working on basic counting, back in 2nd
grade.
There's a fifth, equally ugly, possible solution:
Place the four pennies in a "Y" formation, but draw the lines in a "V"
shape, and consider the pennies to have nonzero size.
A B
C
D
The line AD passes through part of C. The line BD passes through a
different part of C. So I could say that there are three pennies in each
of those lines. It's a bit of a strain, but not much more so than any of
the other four suggestions.
[I've crossposted this to rec.puzzles. The guys there can probably think
of dozens more ugly solutions.]

Mike Williams
Gentleman of Leisure
You can get the same result by placing two pennies beside each other
on the table, touching at an edge, then stacking the other two
centered on the point where the first two touch.
riverman
This is good. Have the AB pair located, say, 3 miles away. The
lines ACD and BCD will then be straight within a measurement error
of .00000001 or so. (didn't actually calculate it)

Mike Kruger
"What information consumes is rather obvious: it consumes the
attention
of its recipients. Hence a wealth of information creates a poverty
of
attention, and a need to allocate that attention efficiently among
the
overabundance of information sources that might consume it." 
Herbert
A. Simon
It would be easy if the question is for four dollars.
Arrange them (2 1dollar coins and 1 2dollar coin as below)
A
BC
Where A and C are 1dollar coins and B is a 2dollar coin.
The four pennies problem is bit more complicated. I have never heard
of a 2penny coin. I can only find a 2 penny stamp from the website
below.
http://commons.wikimedia.org/wiki/Image:1882_Queen_Victoria_2_penny_mauve.JPG
If 'coin' is not the necessary requirement in this problem then we can
replace the 1dollar coins with 1penny stamps and the 2dollar coin
with a 2penny stamp.
Without mentioning the answers already posted, including the intended one!
Not good technique, Mike, unless you're *trying* for a repetitive thread.

Mark Brader  "I thought it was a big joke.
Toronto  Dr. Brader is known for joking around a lot."
m...@vex.net  Matthew McKnight
> It would be easy if the question is for four dollars.
> Arrange them (2 1dollar coins and 1 2dollar coin as below) ...
> The four pennies problem is bit more complicated. I have never heard
> of a 2penny coin.
The original context was US coinage, where "penny" is slang for a 1cent
coin. (Which is a pity for this answer, because of course the US *does*
have 2cent coins. They were last minted in... just a moment... 1873.)
The solution is also impossible in British coinage, because the plural
given was "pennies", not "pence". "Pence" is the only plural used when
the word refers to the unit of currency.
Nice idea, though.

Mark Brader, Toronto "Do right; have fun; make money."
m...@vex.net Ian Darwin on Yuri Rubinsky (195296)
My text in this article is in the public domain.
Or he wants the community there to approach the problem fresh, without
being influenced by other people's solutions.

Please reply to:  "One of the hardest parts of my job is to
pciszek at panix dot com  connect Iraq to the War on Terror."
Autoreply is disabled   G. W. Bush, 9/7/2006
In that font it surely isn't, unless you have an invisible (fifth) penny.

charles, no silver to be seen, bishop
Does his drawing, as seen here, look the same as when you saw it?

chrles
I think you need to get rid of your Commodore 64 computer and get a
modern machine.
Les
>On Sat, 1 Nov 2008 09:01:24 0700, use...@bauerstar.com (Jerry Bauer)
>wrote:
[snip]
>>
>>There's nothing in the problem, as posed, that says that you cannot
>>provide another penny.
>>
>
>That's absolutely right.
>
>So the answer is
>
> 0
>0 0 0
> 0
>
>which indeed consists of four pennies (plus another penny) lined up in
>two straight lines, with three pennies in each line.
One line looks a little bendy.
On a similar theme, I had one of those puzzles that consisted of pieces,
each piece consisted of a few cubes glued together in odd shapes. When
solved the shapes could be put togethr to form a larger cube. A family was
over for dinner one night and their child was working on the puzzle. He
came in to announce that he had "solved" it. Which he had, in a way, by
taking one of the pieces and breaking off a smaller cube so that the
pience (minus a cube) fit and then adding the lone cube to assemble the
larger cube.

charles
Soma Cube?
http://en.wikipedia.org/wiki/Soma_cube
I have a set of those, I made them myself with some wooden cubes, of
which my dad had a large box, and some of the white PVA wood glue.
They've been bashed about over the years (at least 30 of them by now),
and none of the pieces has, so far at least, broken.

Peter
I'm an alien
email: home at peteward dot gotadsl dot co dot uk
Songs like that make we want to commit Sudoku.
 Artyw
>>>> The question was, basically, how can you take four pennies, line
>>>> them up in two straight lines, with three pennies in each line.
>
>> It would be easy if the question is for four dollars.
>> Arrange them (2 1dollar coins and 1 2dollar coin as below) ...
>
>> The four pennies problem is bit more complicated. I have never heard
>> of a 2penny coin.
>
>The original context was US coinage, where "penny" is slang for a 1cent
>coin. (Which is a pity for this answer, because of course the US *does*
>have 2cent coins. They were last minted in... just a moment... 1873.)
>
>The solution is also impossible in British coinage, because the plural
>given was "pennies", not "pence". "Pence" is the only plural used when
>the word refers to the unit of currency.
Not so. In normal usage, four pence is an amount of money, four
pennies is four penny coins.
>Nice idea, though.

Peter
I'm an alien
email: home at peteward dot gotadsl dot co dot uk
All cats are, in a very real sense, in the kitchen meowing for food even when they appear to be somewhere else.
Peter Ward:
> Not so. In normal usage, four pence is an amount of money, four
> pennies is four penny coins.
So, then, by "not so", you mean "exactly".

Mark Brader  "...it's always easier to see the mud when it's
Toronto  coming toward your side rather than from your side."
m...@vex.net  Mike Kruger
Riiight. And you telepathically transmitted to each of us the typeface
to use to make that line up the way you intended.

eben QebWe...@vTerYizUonI.nOetP http://royalty.mine.nu:81
Are you confident that you appear to be professional in your electronic
communication? Consider this: A: No
Q: Can I top post? from ni...@xx.co.uk
> Mark Brader:
>>> The solution is also impossible in British coinage, because the plural
>>> given was "pennies", not "pence". "Pence" is the only plural used when
>>> the word refers to the unit of currency.
>
> Peter Ward:
>> Not so. In normal usage, four pence is an amount of money, four
>> pennies is four penny coins.
>
> So, then, by "not so", you mean "exactly".
Er, no. If a solution is possible at all (and it's trivial  for example,
you can just place coin A on top of coin B, with coins C and D both
touching coin B and CBD forming a right angle), it is possible in British
coinage, using four pennies (four penny coins). The fact that they are
collectively valued at a monetary amount of four pence is irrelevant to
the problem, and I'm surprised you bothered to raise the fact in the first
place.
To illustrate this, let's ask a question with the same structure, but with
a different word in place: "The question was, basically, how can you take
four tanners, line them up in two straight lines, with three tanners in
each line." The fact that four tanners come to two bob is irrelevant to
the problem. And so is the fact that four pennies come to four pence.
Thus your claim "The solution is ... impossible in British coinage" is
incorrect.

Richard Heathfield <http://www.cpax.org.uk>
Email: http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place"  dmr 29 July 1999
Richard Heathfield writes:
> Er, no. If a solution is possible at all...
I said *the* solution, not *a* solution. The solution of using a
coin worth 2 pennies, as given in the post I was responding to.
> (and it's trivial  for example, you can just place coin A on top
> of coin B, with coins C and D both touching coin B and CBD forming
> a right angle),
And so the thread comes full circle, as espected after the carelessly
designed crossposting.
Of course that is *not* a solution to the question as stated, because
no three of the coins are in a straight line. And, of course, it *was*
also the expected answer. And, of course, this was already pointed out
in alt.fan.ceciladams.
> it is possible in British
> coinage, using four pennies (four penny coins). The fact that they are
> collectively valued at a monetary amount of four pence is irrelevant to
> the problem, and I'm surprised you bothered to raise the fact in the first
> place.
It was relevant to the solution that I was responding to. Please read
more carefully.

Mark Brader, Toronto  "Mark is probably right about something,
m...@vex.net  but I forget what"  Rayan Zachariassen