From Newsgroup: rec.puzzles

On 23/08/2025 20:25, Charlie Roberts wrote:

Is this not the Moser Circle Problem, stated in a different manner?

I'd say a variation, but definitely related.
--
David Entwistle
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From Newsgroup: rec.puzzles

On 23/08/2025 09:23, Richard Heathfield wrote:

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Well done. I derive the formula for the number of bits of potato as:
(n^2)/2 + n/2 + 1, where n is the number of cuts.
--
David Entwistle
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From Newsgroup: rec.puzzles

On 23/08/2025 08:35, David Entwistle wrote:

Take a circular slice of potato, place it on the table, and see into how large a number of pieces you can divide it with six cuts of a knife.

Would anyone like to attempt a solution for the maximal division of a
solid, roughly spherical, potato dissected by n planes?

My imagination suggests:

n = 0, 1 piece.
n = 1, 2 pieces.
n = 2, 4 pieces.
n = 3, 8 pieces.

So far so good. At this point I resorted to cutting a real potato, and
with n = 4 got 13 pieces, but as every piece had skin on it, I suspect
my cuts did not result in the maximal number of pieces. 16 suggests
itself as a obvious answer, but I'd not be very confident in that assertion.

Any takers?
--
David Entwistle
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From Newsgroup: rec.puzzles

On 24/08/2025 08:59, David Entwistle wrote:

On 23/08/2025 08:35, David Entwistle wrote:

Take a circular slice of potato, place it on the table, and see
into how large a number of pieces you can divide it with six
cuts of a knife.

Would anyone like to attempt a solution for the maximal division
of a solid, roughly spherical, potato dissected by n planes?

My imagination suggests:

n = 0, 1 piece.
n = 1, 2 pieces.
n = 2, 4 pieces.
n = 3, 8 pieces.

So far so good. At this point I resorted to cutting a real
potato, and with n = 4 got 13 pieces, but as every piece had skin
on it, I suspect my cuts did not result in the maximal number of
pieces. 16 suggests itself as a obvious answer, but I'd not be
very confident in that assertion.

Any takers?

Martin Gardner took a crack at this in a book I (alas) no longer
possess, entitled something like "More Mathematical Recreations
and Diversions" and published in the 17th century IIRC.

He used cocktail sticks to hold some of the pieces in place.

There is, of course, an equation to give the answer to the impatient.
--
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

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From Newsgroup: rec.puzzles

On 24/08/2025 08:59, David Entwistle wrote:

Would anyone like to attempt a solution for the maximal division of a
solid, roughly spherical, potato dissected by n planes?

My second attempt involved wrapping cling film around the three-cut eight-piece potato. I got a solid 14 pieces ...
--
David Entwistle
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From Newsgroup: rec.puzzles

On 24/08/2025 08:59, David Entwistle wrote:

On 23/08/2025 08:35, David Entwistle wrote:

Take a circular slice of potato, place it on the table, and see into
how large a number of pieces you can divide it with six cuts of a knife.

Would anyone like to attempt a solution for the maximal division of a
solid, roughly spherical, potato dissected by n planes?

My imagination suggests:

n = 0, 1 piece.
n = 1, 2 pieces.
n = 2, 4 pieces.
n = 3, 8 pieces.

So far so good. At this point I resorted to cutting a real potato, and
with n = 4 got 13 pieces, but as every piece had skin on it, I suspect
my cuts did not result in the maximal number of pieces. 16 suggests
itself as a obvious answer, but I'd not be very confident in that
assertion.

Any takers?

SPOILER.
POILER.
OILER.
ILER.
LER.
ER.
R.
.

There's a very nice and comprehensive review of the intersection planes problem here:

https://www.themathdoctors.org/cutting-up-space-using-n-planes/

I see my dissection skills aren't yet up to scratch.
--
David Entwistle
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