Puzzle: Cutting a Pizza into 8 pieces with 3 cuts.
Gladywin
Hi all,
How do I cut a pizza into 8 pieces with just 3 cuts? Is it possible to have equal pieces?
By the way, I believe that there should be a compilation of such puzzle book. Does anybody know of any good books on all these type of puzzles? Like the joining of 9 dots with just 4 straight line, etc?
Thanks in advance for any help.
[Pls reply to glad...@singnet.com.sg]
Gladywin
010899
Peter Elsden
<glad...@singnet.com.sg> writes
Try Puzzles 4 Pleasure by Barry R.Clarke published by The Cambridge
University Press ISBN 0 521 46634 2.
It contains "brain twisters" with the book split between Popular puzzles
and Advanced puzzles.
--
Peter Elsden Runaid Enterprises
email: sa...@runaid.co.uk Broxbourne. Herts
www : http://www.runaid.co.uk UK
Brian Skinner
> How do I cut a pizza into 8 pieces with just 3 cuts?
> Is it possible to have equal pieces?
One obvious method: cut the pizza in two and pile the halves. Cut
again giving quarters and pile the quarters. Cut again giving 8 equal
pieces. Mind you, the resulting pieces would be a bit messy, topping
everywhere.
Without rearrangement, only 7 pieces are possible (see
http://www.askdrmath.com/problems/caviness1.18.99.html)
--
Brian
Mike Fenn
pieces, but they won't be equal in composition, just shape. Just cut the pie
in quarters with two cuts, then cut the whole thing through the centre in
the same way you cut a sponge cake to get the icing in. You really need a
deep pan pizza for this to work, and only half your guests get any topping
:-)
Mike.
BOBVL
cartoon character)
When asked , in a pizzeria, if he wanted his personal pizza cut in 4 or 8
pieces, he said "Four...I don't think I can eat eight"
bobvl
Martin Julian DeMello
Or, alternatively, cut it into quarters, then have a ring-shaped cut at the
right distance from the centre to make all 8 pieces of equal area.
--
Martin DeMello
Jeff Jetton
mdem...@pound.ruf.rice.edu writes:
>Or, alternatively, cut it into quarters, then have a ring-shaped cut at the
>right distance from the centre to make all 8 pieces of equal area.
That makes a simple little math puzzle in itself, albeit an increasingly
off-topic one. How do you find the right distance from the center?
SPOILER SPACE
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As far as I can tell... take the radius of the pizza and divide by the
square root of two. That's how big you need to make the radius of the
inner circle to get the areas equal. Or, to put it another way, measure
the diameter of the pizza, divide by the square root of two, subtract
that from the original diameter, divide by two... that's how far in the
inner circle needs to be from the "crust".
But hey, if you're allowing non-straight cuts, I know of at least one way
you could cut it into eight pieces with only two cuts--one straight, one
curvy. There's probably even a way to make all the areas equal too, but
danged if I could do the math on that. :)
- Jeff
Mike Fenn
tracking across the pizza in a zig-zag. Speaking of going off-topic, how do
you cut a Topic into 8 equal pieces so that each piece has the same number
of hazelnuts in it?
Mike.
Robert Arthur
Brian Skinner wrote:
> Gladywin <glad...@singnet.com.sg> wrote:
>
> > How do I cut a pizza into 8 pieces with just 3 cuts?
> > Is it possible to have equal pieces?
>
> One obvious method: cut the pizza in two and pile the halves. Cut
> again giving quarters and pile the quarters. Cut again giving 8 equal
> pieces. Mind you, the resulting pieces would be a bit messy, topping
> everywhere.
Instead of piling, one could lay the quaters into a row...
> Without rearrangement, only 7 pieces are possible
As long as you restrict yourself to straight lines this is true.
Halfing, halfing again then making a circular cut about 7/10 the radius
of the whole pizza round the centre will produce 8 roughly equal-area
pieces.
Bob.
Brian Skinner
> Brian Skinner wrote:
>
> > Without rearrangement, only 7 pieces are possible
>
> As long as you restrict yourself to straight lines this is true.
> Halfing, halfing again then making a circular cut about 7/10 the radius
> of the whole pizza round the centre will produce 8 roughly equal-area
> pieces.
If you allow non-straight cuts, then you can produce N equal-area
pieces with a single cut. There are an infinite number of possible
ways of doing this.
--
Brian
Jeff Jetton
br...@brisk.demon.co.uk writes:
>If you allow non-straight cuts, then you can produce N equal-area
>pieces with a single cut. There are an infinite number of possible
>ways of doing this.
I'll be picky here and disagree. In order to cut the pizza into more than
two pieces with a single cut, you have to go "off the pizza" and come
back in, even if only for one pizza molecule's worth. To me, that counts
as a separate cut, even if you don't have to lift the cutter.
- Jeff, splitting hairs along with his pizzas
BOBVL
(laughter) / (Internal RevenueService)
[They're doing it when auditing your return]
(9,5)
===============
>Subject: Re: Puzzle: Cutting a Pizza into 8 pieces with 3 cuts.
>From: Jeff Jetton jet...@REMOVETHISmindspring.com
>Date: Tue, 03 August 1999 06:36 PM EDT
>Message-id: <7o7qtg$k97$1...@nntp3.atl.mindspring.net>
Robert Arthur
Brian Skinner wrote:
> Robert Arthur <r...@st-and.ac.uk> wrote:
> > As long as you restrict yourself to straight lines this is true.
> > Halfing, halfing again then making a circular cut about 7/10 the radius
> > of the whole pizza round the centre will produce 8 roughly equal-area
> > pieces.
>
> If you allow non-straight cuts, then you can produce N equal-area
> pieces with a single cut. There are an infinite number of possible
> ways of doing this.
Not with a single cut - however, I believe we have already crossed the
boundries of padantry. Fun, innit?
Bob.
Brian Skinner
> In article <37af2609...@news.demon.co.uk> Brian Skinner,
> br...@brisk.demon.co.uk writes:
> >If you allow non-straight cuts, then you can produce N equal-area
> >pieces with a single cut. There are an infinite number of possible
> >ways of doing this.
>
> I'll be picky here and disagree. In order to cut the pizza into more than
> two pieces with a single cut, you have to go "off the pizza" and come
> back in, even if only for one pizza molecule's worth.
No, it's possible to cut the pizza into N equal-area pieces with a
single cut without the cutter meeting the edge of the pizza.
--
Brian
Jeff Jetton
br...@brisk.demon.co.uk writes:
>No, it's possible to cut the pizza into N equal-area pieces with a
>single cut without the cutter meeting the edge of the pizza.
Ah yes. I hadn't considered cuts that come back to cross themselves. Is
that what you were thinking?
- Jeff
"This particular poster represents a short education in a certain way of
breathing (6)"
Brian Skinner
> In article <37acf9d4...@news.demon.co.uk> Brian Skinner,
> br...@brisk.demon.co.uk writes:
> >No, it's possible to cut the pizza into N equal-area pieces with a
> >single cut without the cutter meeting the edge of the pizza.
>
> Ah yes. I hadn't considered cuts that come back to cross themselves. Is
> that what you were thinking?
Yes, that's the idea (but more generally, curves that come back to
meet themselves). If you want to divide the pizza into three
equal-area parts with a single cut, one easy way is to cut a
figure-of-eight of appropriate size and shape. To divide it into four,
you could cut a curve-like-a-figure-of-eight-but-with-three-loops,
etc.
--
Brian
Brian Skinner
> (laughter) / (Internal RevenueService)
>
> [They're doing it when auditing your return]
>
> (9,5)
Splitting hairs: Can "ha" be used for laughter, or should it be "haha"
or "ha-ha"?
--
Brian
BOBVL
>From: br...@brisk.demon.co.uk (Brian Skinner)
>Date: Wed, 04 August 1999 01:40 PM EDT
>Message-id: <37ac76f7...@news.demon.co.uk>
If it is not very funny (like my clue) a single ha suffices...
Seriously, folks, Chambers and American Heritage both indicate ha should be
repeated to indicate laughter, but Websters New Universal Unabridged gets me
off the hook:
"ha...the sound of the exclamation ha or of a laugh"
It seems I have the last ha
BobVL, FL
Ucalegon
Skinner) writes:
>> Ah yes. I hadn't considered cuts that come back to cross themselves. Is
>> that what you were thinking?
>
>Yes, that's the idea (but more generally, curves that come back to
>meet themselves).
And without self-intersection you can always do it with two:
a straight cut and one that loops back and forth across it.
Acag, Treesong (ucal...@aol.com)
Wei-Hwa Huang
>Yes, that's the idea (but more generally, curves that come back to
>equal-area parts with a single cut, one easy way is to cut a
>figure-of-eight of appropriate size and shape. To divide it into four,
>you could cut a curve-like-a-figure-of-eight-but-with-three-loops,
>etc.
But then some poor sap gets all the crust! That's not very fair!
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
---------------------------------------------------------------------------
It's not sarcasm. It's reductio ad absurdum.
Jeff Jetton
But then all those other poor saps don't get any crust! That's not very
fair! :)
- Jeff, lover of crust