2 ten foot planks/12 foot moat width math question
Scott Royer
points/questions have been brought up before, my apologies and can you
point me to a place where I can view these points/questions?
The question revolves around this puzzle:
Your friend is stranded on an a square island surrounded by a square
moat that is 12 feet wide. You have two 10 feet long planks. How can
you build a bridge using only the planks to rescue your friend?
The traditional answer is to place the planks in a T-shape in one corner
of the moat.
I post puzzles here at work on a whiteboard and thought that this one
might be too easy, so I added two other parts to the puzzle:
2. Assuming neglible overlap, what length of planks are over the water?
3. How far would you have to walk to build the bridge?
After a length discussion about number 2, several co-workers and myself
came to the conclusion that the first solution to the puzzle does not
work, based on these ideas:
Distance from corner of island to corner of moat = sqrt(12^2 + 12^2) =
~16.97
Distance from corner of moat to t-cross portion of bridge =
sqrt((5*sqrt(2))^2 - 5^2) = 5
Distance from corner of island to t-cross portion of bridge = 16.97 - 5
= 11.97
The obvious problem with this is that the plank is only ten feet long
and would thus not fit.
Several co-workers and myself came to these same results independantly.
Are we all making the same mistake in our calculations or is there
something we're missing in this puzzle?
Thanks,
Scott
Parallax
wrote:
<snip most of description of puzzle>
>The question revolves around this puzzle:
>
>Your friend is stranded on an a square island surrounded by a square
>moat that is 12 feet wide. You have two 10 feet long planks. How can
>you build a bridge using only the planks to rescue your friend?
>
>Several co-workers and myself came to these same results independantly.
>Are we all making the same mistake in our calculations or is there
>something we're missing in this puzzle?
You may be making the mistake that the moat is 10 feet wide and the
planks are 9 feet long. That's the puzzle I solved when I was working
on it. Maybe 9 1/2 feet long... Don't remember.
--Parallax
Sweeping generalizations always have exceptions, even this one.
Dave Seaman
Scott Royer <sco...@hamsoft.com> wrote:
>Your friend is stranded on an a square island surrounded by a square
>moat that is 12 feet wide. You have two 10 feet long planks. How can
>you build a bridge using only the planks to rescue your friend?
>The traditional answer is to place the planks in a T-shape in one corner
>of the moat.
That method works if the width of the moat is less than 3/4 * sqrt(2) *
(length of plank). For a 10 ft. plank, that works out to about 10.6 feet
as the maximum width of a moat that can be crossed.
--
Dave Seaman dse...@purdue.edu
Stay of execution granted for Mumia Abu-Jamal.
<http://mojo.calyx.net/~refuse/altindex.html>
Martin Julian DeMello
> Your friend is stranded on an a square island surrounded by a square
> moat that is 12 feet wide. You have two 10 feet long planks. How can
> you build a bridge using only the planks to rescue your friend?
> The traditional answer is to place the planks in a T-shape in one corner
> of the moat.
<snip>
> Distance from corner of island to corner of moat = sqrt(12^2 + 12^2) =
> ~16.97
> Distance from corner of moat to t-cross portion of bridge =
> sqrt((5*sqrt(2))^2 - 5^2) = 5
> Distance from corner of island to t-cross portion of bridge = 16.97 - 5
> = 11.97
> The obvious problem with this is that the plank is only ten feet long
> and would thus not fit.
You're right - it won't work! Interesting; it seems counterintuitive (at
least I never thought to verify the 10/12 solution). The first pair for
which it will work, in fact, are 19 and 20 (you get y sqrt(8/9) < x < y, and
sqrt(8/9) is .9428.. or just under 19/20).
--
Martin DeMello
Walter Prager
"obvious" way.
However, if the moat is 8' deep you can use one of the planks to "pole-vault"
across it. Or, fashion the planks into stilts.
I also heard a variation of the puzzle where you had a supply (rather than
just two) of these planks. Three more should get you across.
--
Walter Prager, S/W Designer | ||| "I don't have all the answers. In
TEL: (613) 599-3600 ext 6460 | |||||||| life, to be honest, I've failed as
EMAIL: wpr...@newbridge.com | ||||\||| much as I've succeeded. But I love
| ||||\\|| my wife, I love my life, and I wish
NEWBRIDGE NETWORKS CORP | ||||\\\| you *my* kind of success."
Kanata, Ontario, Canada | ||| Dicky Fox
Lynn Johannesen
: I also heard a variation of the puzzle where you had a supply (rather than
: just two) of these planks. Three more should get you across.
Dudeney's "Canterbury Puzzles" (1929) gives you 8 9-foot planks and
a 10-foot moat. (I suspect this is actually the original, which has
been corrupted into something unsolvagry over the years.)
Rich Grise
I saw a version of this with a square island in the middle of the
square moat, and two planks, not long enough to span the moat, but
they had a solution. This was 40 years ago, or so, so I don't
remember the dimensions, more's the pity. Their solution was to
put one plank diagonally, then the other from the middle of it
to the island. But I did a little trig, and it won't work with
2 - 10' planks and a 12' moat.
Does the guy have a drill and some bolts?
Cheers!
Rich
bbarth...@voltdelta.com
Lynn Johannesen <ly...@netcom9.netcom.com> wrote:
> Walter Prager <wpr...@newbridge.com> wrote:
> : I also heard a variation of the puzzle where you had a supply
(rather than
> : just two) of these planks. Three more should get you across.
>
> Dudeney's "Canterbury Puzzles" (1929) gives you 8 9-foot planks and
> a 10-foot moat. (I suspect this is actually the original, which has
> been corrupted into something unsolvagry over the years.)
>
and a 12 foot moat, can you span the moat? What is the minimum number
of planks needed?
--
Bruce Bartholomew
Riverside, CA
Sent via Deja.com http://www.deja.com/
Before you buy.
Scott Royer
accompaning picture):
"You friends are stranded in the middle of the park's pond. You have two 10
foot planks, but it is 12 foot to the island. How can you rescue them?"
We've (my co-workers and I) come to the conclusion that the minimum length
of the boards need to create the T-cross bridge at the corner is 2/3 *
(width of moat) * sqrt(2). Acording to this formula, for a 12-foot moat,
you would need planks at least 11 1/3 feet long; for a 10-foot moat, ~9.4
feet long.
None of these calculations take into effect the width of the boards;
however, the boards would need to be pretty wide (2 feet at least, if memory
serves correctly) in order to reach.
Scott
Parallax wrote:
> On Tue, 09 Nov 1999 11:28:10 -0800, Scott Royer <sco...@hamsoft.com>
> wrote:
>
> <snip most of description of puzzle>
>
> >The question revolves around this puzzle:
> >
> >Your friend is stranded on an a square island surrounded by a square
> >moat that is 12 feet wide. You have two 10 feet long planks. How can
> >you build a bridge using only the planks to rescue your friend?
> >
Walter Prager
>
> The puzzle, as stated, is a trick question -- it cannot be done in the
> "obvious" way.
>
> However, if the moat is 8' deep you can use one of the planks to "pole-vault"
> across it. Or, fashion the planks into stilts.
In fact, with two planks you can place one diagonally across, and this be able
to vault across a moat even wider than 12 feet (or deeper, as long as it's
less than 10').
>
> I also heard a variation of the puzzle where you had a supply (rather than
> just two) of these planks. Three more should get you across.
--
Red Dorakeen
<bbarth...@voltdelta.com> wrote in message
news:80ci7g$bjd$1...@nnrp1.deja.com...
| In article <80c44e$71m$4...@nntp8.atl.mindspring.net>,
| Lynn Johannesen <ly...@netcom9.netcom.com> wrote:
| > Walter Prager <wpr...@newbridge.com> wrote:
| (rather than
| > : just two) of these planks. Three more should get you across.
| >
| > a 10-foot moat. (I suspect this is actually the original, which has
| > been corrupted into something unsolvagry over the years.)
| >
| So follow-up question for 10/12 is: Given a supply of 10 ft. planks
| and a 12 foot moat, can you span the moat? What is the minimum number
| of planks needed?
I still like fashioning two planks into stilts and walking across. Or make
some waterskis....get shot out of a cannon, and skip across the moat no
problem..
Cheers,
Red
Jim Hewitt
>
> I got the puzzle from BrainBashers.com. The exact wording is (with
> accompaning picture):
>
> "You friends are stranded in the middle of the park's pond. You have two 10
> foot planks, but it is 12 foot to the island. How can you rescue them?"
>
> We've (my co-workers and I) come to the conclusion that the minimum length
> of the boards need to create the T-cross bridge at the corner is 2/3 *
> (width of moat) * sqrt(2). Acording to this formula, for a 12-foot moat,
> you would need planks at least 11 1/3 feet long; for a 10-foot moat, ~9.4
> feet long.
>
> None of these calculations take into effect the width of the boards;
> however, the boards would need to be pretty wide (2 feet at least, if memory
> serves correctly) in order to reach.
>
How deep is the moat? One could conceivably put one plank on shore sticking into
the water. As long as more than two feet of the plank is still above water, you
can run the other plank form the island to it. Or maybe the people can just jump
the foot or two or three? that remain underwater?
Jim
PS Are we allowed to use our belt to connect the two?
> Scott
>
> Parallax wrote:
>
> > On Tue, 09 Nov 1999 11:28:10 -0800, Scott Royer <sco...@hamsoft.com>
> > wrote:
> >
> > <snip most of description of puzzle>
> >
> > >The question revolves around this puzzle:
> > >
> > >Your friend is stranded on an a square island surrounded by a square
> > >moat that is 12 feet wide. You have two 10 feet long planks. How can
> > >you build a bridge using only the planks to rescue your friend?
> > >
> > >Several co-workers and myself came to these same results independantly.
> > >Are we all making the same mistake in our calculations or is there
> > >something we're missing in this puzzle?
> >
> > You may be making the mistake that the moat is 10 feet wide and the
> > planks are 9 feet long. That's the puzzle I solved when I was working
> > on it. Maybe 9 1/2 feet long... Don't remember.
> >
> > --Parallax
> >
> > Sweeping generalizations always have exceptions, even this one.
--
Jim Hewitt, Software Design Engineer
Hewlett-Packard Co., Department LaserJet Division
(208)-396-4417 Jim_H...@hp.com
Rich Grise
bbarth...@voltdelta.com wrote:
>
> In article <80c44e$71m$4...@nntp8.atl.mindspring.net>,
> Lynn Johannesen <ly...@netcom9.netcom.com> wrote:
> > Walter Prager <wpr...@newbridge.com> wrote:
> > : I also heard a variation of the puzzle where you had a supply
> (rather than
> > : just two) of these planks. Three more should get you across.
> >
> > Dudeney's "Canterbury Puzzles" (1929) gives you 8 9-foot planks and
> > a 10-foot moat. (I suspect this is actually the original, which has
> > been corrupted into something unsolvagry over the years.)
> >
> So follow-up question for 10/12 is: Given a supply of 10 ft. planks
> and a 12 foot moat, can you span the moat? What is the minimum number
> of planks needed?
> --
> Bruce Bartholomew
> Riverside, CA
I think I could do it in three planks. Assuming the moat is square,
the dimension from the corner of the moat to the corner of the island
is something over 16 feet. So, you do the diagonal one, then put
a second one perpendicular to it, but with its end at the right
angle "behind" it. You could hang a good 4 feet of plank over the
end, then reach out with the third one, somebody on the island
positions it so its end lies on top of the second diagonal one,
then you walk back and stand on the end of the second one, that's
on solid ground, so the long end is kind of cantilevered. Then they
walk across the two planks.
| |
| <- corner of |
----\ island |
\ |
\ |
overlap -> \\ /|
\ / |
cantilever -> \ / |
/ \ |
/ \ |
/ \|
------------------------O <- stand here
Cheers!
Rich
fred klein
>
> This question is regarding a (I assume) well-known puzzle and if these
> points/questions have been brought up before, my apologies and can you
> point me to a place where I can view these points/questions?
>
>
> Your friend is stranded on an a square island surrounded by a square
> moat that is 12 feet wide. You have two 10 feet long planks. How can
> you build a bridge using only the planks to rescue your friend?
1) Throw one plank to your friend on the island. Place the other
plank so one end sticks 4' out over the water, and stand on the
other end. Friend then places their plank from the island to the
end of your plank, and walks across.
Pardon my ascii (not really to scale):
YOU _______________________theirs
Yours ------------------------
********************** ***********
********************** ***********
Shore Island
2) Bind the two together somehow- belt, rope, whatever- into a
plank long enough to reach.
Fred Klein
tubl...@gmail.com
> This question is regarding a (I assume) well-known puzzle and if these
> points/questions have been brought up before, my apologies and can you
> point me to a place where I can view these points/questions?
>
> The question revolves around this puzzle:
>
> Your friend is stranded on an a square island surrounded by a square
> moat that is 12 feet wide. You have two 10 feet long planks. How can
> you build a bridge using only the planks to rescue your friend?
>
> of the moat.
>
> might be too easy, so I added two other parts to the puzzle:
>
> 2. Assuming neglible overlap, what length of planks are over the water?
>
> 3. How far would you have to walk to build the bridge?
>
> work, based on these ideas:
>
> ~16.97
>
> Distance from corner of moat to t-cross portion of bridge =
> sqrt((5*sqrt(2))^2 - 5^2) = 5
>
> Distance from corner of island to t-cross portion of bridge = 16.97 - 5
> = 11.97
>
> The obvious problem with this is that the plank is only ten feet long
> and would thus not fit.
>
> Are we all making the same mistake in our calculations or is there
> something we're missing in this puzzle?
>
>
> Scott
Wouldn't it matter the width of the planks. A 2 foot wide plank would extend farther from corner of moat to make up for the 1.97 feet that is needed to make original solution work.
Brian Tung
> Wouldn't it matter the width of the planks. A 2 foot wide plank would
> extend farther from corner of moat to make up for the 1.97 feet that is
> needed to make original solution work.
Here's a link to the Google (originally Deja Vu) archive of this thread.
Discussed at length. I like Fred Klein's solution.
--
Brian Tung <brian....@gmail.com>
The Astronomy Corner at http://www.astronomycorner.net/
Astronomical Games at http://www.astronomycorner.net/games/
My Own Personal FAQ at http://www.astronomycorner.net/reference/faq.html
David B
news:<lmbu6d$m6o$1...@speranza.aioe.org>...
> > Wouldn't it matter the width of the planks. A 2 foot wide plank would
> > extend farther from corner of moat to make up for the 1.97 feet that is
> > needed to make original solution work.
>
> Did you really mean to resurrect a fifteen-year-old thread?
>
> Here's a link to the Google (originally Deja Vu) archive of this thread.
> Discussed at length. I like Fred Klein's solution.
>
www.dejanews.com
D
Brian Tung
> Did you really mean to resurrect a fifteen-year-old thread?
>
> Here's a link to the Google (originally Deja Vu) archive of this thread.
> Discussed at length. I like Fred Klein's solution.
> I think you'll find it was DejaNews not Deja Vu.
slightly odd way of putting it.)
Irrespective of that, it's a strange piece of thread necromancy.
David B
> > Did you really mean to resurrect a fifteen-year-old thread?
> >
> > Here's a link to the Google (originally Deja Vu) archive of this thread.
> > Discussed at length. I like Fred Klein's solution.
>
> David B wrote:
> > I think you'll find it was DejaNews not Deja Vu.
>
> You're right, I misremembered. (Although "I think you'll find" is a
> slightly odd way of putting it.)
Where do you come from?
>
> Irrespective of that, it's a strange piece of thread necromancy.
>
--
Brian Tung
> Is it?
> Where do you come from?
mscot...@gmail.com
> > > >
> > > >Your friend is stranded on an a square island surrounded by a square
> > > >moat that is 12 feet wide. You have two 10 feet long planks. How can
> > > >you build a bridge using only the planks to rescue your friend?
> > > >
> > > >Are we all making the same mistake in our calculations or is there
> > > >something we're missing in this puzzle?
> > >
> > > planks are 9 feet long. That's the puzzle I solved when I was working
> > > on it. Maybe 9 1/2 feet long... Don't remember.
> > >
> > > --Parallax
> > >
> > > Sweeping generalizations always have exceptions, even this one.
>
> --
> Jim Hewitt, Software Design Engineer
> Hewlett-Packard Co., Department LaserJet Division
> (208)-396-4417 Jim_H...@hp.com
Richard Heathfield
<why not? I've got five minutes>
>>>>> Your friend is stranded on an a square island surrounded by a square
>>>>> moat that is 12 feet wide. You have two 10 feet long planks. How can
>>>>> you build a bridge using only the planks to rescue your friend?
SSSSS S = shore
SMMMS M = moat
SMIMS I = island
SMMMS
SSSSS
I modelled this in a 3D wossname, and it didn't take long for me to
convince myself that you can't just lay the first plank across the
corner of the moat and use that as a support for the second plank, no
matter what angles you try. So a more creative solution is called for.
My stranded friend saw me arrive. I asked him to hurl the saw across the
moat. (It took several attempts. Eventually we agreed that, instead of
departing and arriving each time, I would just wave, as it would be a
lot quicker.)
My stranded friend saw me wave. He hurled the saw across the moat, and I
used it to saw one of the planks in two, lengthways, thus giving me two
'diet' planks, half as wide but just as long and just as strong (thick):
Full-fat plank:
A--------------------------C
+oooooooooooooooooooooooooo+
+oooooooooooooooooooooooooo+
+oooooooooooooooooooooooooo+
+oooooooooooooooooooooooooo+
B--------------------------D
Diet planks:
E--------------------------G
+oooooooooooooooooooooooooo+
F--------------------------H
I--------------------------K
+oooooooooooooooooooooooooo+
J--------------------------L
It is a little-known fact that I am the caber champion in my local area
(which isn't difficult in my local area, since I'm the only one around
here that has a caber), so I was easily able to throw one of the
slimmed-down planks (EFGH) to my friend.
I now placed the full-fat plank at 45 degrees across the corner of the
moat, such that all four corners A B C and D were on solid ground. Then
I laid the other diet plank across it at right angles, with one end
resting on the very corner of the moat, such that I and J were both on
solid ground. I stood on this end to hold it stable.
My friend then placed his plank on the corner of the island, and
carefully fed it out until, with E and F both firmly on solid ground,
the plank rested on top of the projecting end of the plank on the other
end of which I was standing, and there was easily enough overlap between
GH and KL that he could trot lightly over to safety.
ObPuzzle: what was the maximum possible overlap?
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within
