In the dice game "Petals Around the Rose", what rule gives the answer for each roll of six dice?

Do NOT post the solution method here.  Instead, if you feel like showing
you know it, post a few more rolls of the dice with the answers for
those rolls instead.  This is the kind of puzzle you feel terrible about
if you don't find it yourself.

The student said that his teacher stated he could teach a fourth grader
to do it.  I remember teaching first graders to solve the problem, just
to perplex their parents.

-- John (THEMAZEMAN) <John@www.MAZES.com>

In answer to "I don't get this clue: Rule # 1: The name of the game is
very important":

Gnxr n ybbx ng gur qvpr;  n qvpr vf n ebfr vs vg unf n prageny fcbg,
naq gur ahzore bs crgnyf vf gur ahzore bs fcbgf nebhaq gur prageny
crgny.

-- Courtenay Footman <cpf@lightlink.com>

[ Editor: the hint above is in rot13. ]

History of the puzzle:

Over twenty years ago, I read an article in the National Council of
Teachers of Mathematics "Mathematics Teacher" or "Arithmetic Teacher"
magazine (don't remember which one) detailing this puzzle.  At the
time, I was a member.  As I recall, it was old then. [...]

It's a neat puzzle.  I used to carry dice in my pocket just to bother
kids with it, and wrote an IBM program to simulate the rolling of the
dice.  It never gave the method, but gave unlimited answers.

As I recall, you became "potentate of the rose" by solving six in a row
without a mistake.

-- John (THEMAZEMAN), in mail to Chris Cole

The article "The Petals Around the Rose" was published in the
Mathematics Teacher December 1978 pp 753-54.  It was written by Kurt A
Christoff, Wheeling IL.  In the article he claims to have heard of the
game from George Martin in Madison WI who said that the game was
sweeping through the underground of computer programmers.

-- Joan Armistead <jarmistead@nctm.org>, Senior Journal Editor, NCTM

[ Editor: a five-dice version, from the rec.puzzles thread "Puzzle from
'Hard Drive'", September 1994. ]

In reading Hard Drive recently I came across the following:-

"a dice game called 'Petal Around the Rose'.  The game was developed by
students at USC.  Five dice are thrown, and the player is told 3
things, the name of the game is 'Petal around the Rose', the answer is
always even, and there is a correct answer for each throw of the dice.
The player is told nothing else.  If someone gets the right answer five
times in a row then it is considered prima facie evidence that they
understand the game and they are sworn to secrecy."

OK, I don't understand this game, so can anyone out there help me out.
Give me a few right answers, for a few throws of the 5 dice, and I'll be
able to work it out, I'm sure !!

-- Kevin Maguire <k.maguire@qub.ac.uk>

spurdy@pomona.claremont.edu wrote:
:       This is a puzzle which I have tried unsuccessfully to collect a
: large number of.  I call them misdirection puzzles, and would be
: willing to take replies once again.  The basic premises are that one
: or two people know the secret that explains their ability to
: understand exactly what is going on.  They can perform the action
: (roll the dice in this case) and then take guesses until someone else
: figures it out, then they all get to act superior to those who don't
: know.  The biggest difference between these and Jed's situation
: puzzles is that these generally require a prop.  As for the petals of
: the rose...
:
:       13513=8
:       42635=6
:       41264=0
:       45235=10
:       63214=2
:
:       I don't generally tell them that the answer is always even,
: though.

This suggests to me the numbers on the dice are not important, and
only used as a distraction ??

Is it true that re-ordering has no effect?  ie.

11335=8 ?
23456=6 ?
12446=0 ?
12455=10 ?
12346=2 ?

As you can see I'm still struggling :-(  An email respondent suggests
the numbers should be split into 2 sets (petals and rose obviously!),
and then combined (in his words) "in the obvious way"  Not obvious to
me either which 4 are petals, nor what the 'obvious' combination should
be.

-- Kevin Maguire <k.maguire@qub.ac.uk>

Enough.  The answer is that the number is the number of pips that are
'petals' on dice whose dot patterns have a single dot in the center and
other dots surrounding it.  Therefore, 3 counts as 2 and 5 counts as 4,
the other numbers counting 0.

-- Ken Arromdee <arromdee@jyusenkyou.cs.jhu.edu>

[ Editor: Dick Adams's summary of a 1994 rec.puzzles thread on the
game (five dice there), posted under "Puzzle from 'Hard Drive'". ]

For the benefit of those who have not read the full thread on this
puzzle - Here it is with minor editing and a shorter line length:

kmaguire@main (Kevin Maguire) started it with:
> In reading Hard Drive recently I came across the following:-
> "a dice game called 'Petal Around the Rose'.  The game was
> developed by students at USC.  Five dice are thrown, and the
> player is told 3 things, the name of the game is 'Petal around
> the Rose', the answer is always even, and there is a correct
> answer for each throw of the dice.  The player is told nothing
> else.  If someone gets the right answer five times in a row
> then it is considered prima facie evidence that they understand
> the game and they are sworn to secrecy."
>
> OK, I don't understand this game, so can anyone out there help
> me out. Give me a few right answers, for a few throws of the 5
> dice, and I'll be able to work it out, I'm sure !!

positron@Starbase.NeoSoft.COM (Jonathan Haas) replied:
> Okay, no problem.
>
> 6 3 2 6 3   -> 18
> 5 1 3 3 4   -> 12
> 1 2 4 2 3   -> 10
>
> That enough for you to go on?

spurdy@pomona.claremont.edu replied to Kevin Maguire with:
> This is a puzzle which I have tried unsuccessfully to collect a
> large number of.  I call them misdirection puzzles, and would
> be willing to take replies once again.  The basic premises are
> that one or two people know the secret that explains their
> ability to understand exactly what is going on. They can
> perform the action (roll the dice in this case) and then take
> guesses until someone else figures it out, then they all get to
> act superior to those who don't know.  The biggest difference
> between these and Jed's situation puzzles is that these
> generally require a prop.  As for the petals of the rose...
>
> 13513=8
> 42635=6
> 41264=0
> 45235=10
> 63214=2
>
> I don't generally tell them that the answer is always even,
> though.

spurdy@pomona.claremont.edu replied to Jonathan Haas with
>>  6 3 2 6 3   -> 18
>>  5 1 3 3 4   -> 12
>>  1 2 4 2 3   -> 10

> Okay, this is slightly different than mine, but someone's been
> playing "She loves me, she loves me not" with your roses
> Jonathan.  Mine are still growing.  I hope that was cryptic
> enough not to give away the answer, but sane enough to make
> sense to Jonathan.
>
> My answers for these three are 4, 8, & 2.  I don't remember
> what I posted, so I can't say what Jonathan's answers for mine
> would be.

rex@cq-pan.cqu.edu.au (Rex Boggs) replied to Kevin Maguire with:
> Sure.  As a Potentate of the Rose, I am qualified to do this:
>
>  2  3  2  5  4                  answer - 6
>  1  2  6  6  5                  answer - 4
>  3  2  3  1  4                  answer - 4
>  1  4  2  6  1                  answer - 0
>
> And one more,
>
>  2  5  3  1  5                  answer - 10
>
> Test:  What are the answers to:
>
>  1  2  3  4  5  ?
>  2  3  6  1  3  ?
>  6  6  3  1  2  ?
>  5  6  3  3  5  ?
>  2  6  1  1  1  ?

hoeij@sci.kun.nl (Mark van Hoeij) replied to Kevin Maguire with:
> I'm not completely sure I got it right, but my guess is that
> for the dice:  1 2 3 4 5 the answer is 6 and for: 2 2 4 4 5 the
> answer is 4.

> ... spoiler deleted

kmaguire@main (Kevin Maguire) came back with:

> This suggests to me the numbers on the dice are not important,
> and only used as a distraction??
> ...
> Is it true that re-ordering has no effect?
>
> As you can see I'm still struggling :-(  An email respondent
> suggests the numbers should be split into 2 sets (petals and
> rose obviously!), and then combined (in his words) "in the
> obvious way"  Not obvious to me either which 4 are petals, nor
> what the 'obvious' combination should be.

pwb@cbnewsf.cb.att.com (paul.w.bunting) offered the following:
> The five dice can be split into 2 groups - even and odd.  One
> of those groups has an odd number of dice.  Pick the group with
> the odd number of dice and somehow (?) eliminate one of them.
> The answer is the sum of the others.

arromdee@jyusenkyou.cs.jhu.edu (Ken Arromdee) replied:
> Spoiler deleted

owebster@cris.com (Oren C. Webster) responded to Jonathan Haas with:
> Thanks, Jonathan.
>
>    2 4 1 6 5  ->  16
>    2 1 1 6 3  ->  10
>    1 2 3 3 3  ->   8
>    4 6 2 1 2  ->  14
>    2 5 5 3 6  ->  18
>
> Mum's the word.

rdadams@ubmail.ubalt.edu (Dick Adams) wrote:
> The name of the game is "Petal around the Rose"
> -----------------------------------------------------------
> Prior contributors wrote    |  But alas the correct answers
>                             |
>     6  3  2  6  3  ->  18   |  ->  4
>     5  1  3  3  4  ->  12   |  ->  8
>     1  2  4  2  3  ->  10   |  ->  2
>     2  4  1  6  5  ->  16   |  ->  4
>     2  1  1  6  3  ->  10   |  ->  2
>     1  2  3  3  3  ->   8   |  ->  6
>     4  6  2  1  2  ->  14   |  ->  0
>     2  5  5  3  6  ->  18   |  -> 10

owebster@cris.com (Oren C. Webster) responded to Dick Adams with
> ... petulant personal attack deleted

rdadams@ubmail.ubalt.edu replies:
This thread has split into two different games:
-----------------------------------------------
|             |  Petal around  |  Petals But  |
|  DICE       |    the Rose    |   No Stems   |
|-------------|----------------|--------------|
|  1 1 2 3 6  |        2       |      10      |
|  1 1 3 3 5  |        8       |       8      |
|  1 1 4 5 6  |        4       |      14      |
|  1 2 3 4 5  |        6       |      12      |
|  1 2 4 5 6  |        4       |      14      |
|  1 3 4 5 6  |        6       |      16      |
|  1 4 4 5 5  |        8       |      16      |
|  2 2 3 3 5  |        8       |      12      |
|  2 3 3 4 6  |        4       |      16      |
|  2 4 4 5 6  |        4       |      20      |
|  3 3 4 4 5  |        8       |      16      |
|  3 3 4 5 6  |        8       |      18      |
-----------------------------------------------

-- Dick Adams <rdadams@ubmail.ubalt.edu>, September 1994

[ Editor: Jonathan Haas's spoiler in the September 1994 thread "Puzzle
from 'Hard Drive'", quoted above. ]

Warning: spoilers for this 'game' follow.  If you don't want to know how
it works, don't read any further.

Two different "versions" have been posted.  The way they work is:

      If a die shows a:     1  2  3  4  5  6
      Add to the total:     0  2  2  4  4  6
      Or for version 2:     0  0  2  0  4  0

It's called "petals around the rose" because the number you add
corresponds to the number of pips around the center of the die.
Version 1 has you add all non-central pips to the total.  Version 2 has
you only add non-central pips to the total if a central pip exists.

-- Jonathan S. Haas <positron@neosoft.com>