Math Is Fun Forum

nalareddep

Member

Registered: 2011-09-10

Posts: 2

Double 6 Start

Hi

I have to confess to having failed to solve this problem that has puzzled me regarding dominoes.

I was playing a game with a double 6 set of dominoes called Fives and Threes with 3 friends

The essence of the game is that any ends that can be divided by 3 or/and 5 give points e.g. double six with a 63 attached adds to 15 so = 8 points as it is divided by both 5 and 3 but that information is for interest only at this stage, but what I would like to know is how to calculate the number of possible permutations of the first 4 dominoes can be played following the first player placing the double 6 as the starting domino. e.g one would be 66 then 65 then 53 then 33 how many others are there ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Double 6 Start

hi nalareddep

Welcome to the forum.  I'd start this calculation like this (see picture)

Bob

But there will be lots of branches, so I'll have a think about how to simplify it.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Double 6 Start

hi bob

i'm not sure i am getting this.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Double 6 Start

Not sure what you are not getting so I'll start at the beginning.

A domino is a wooden block twice as long as wide and fairly thin.  A double six set has all possible pairs; that's 28 altogether from (6,6) down to (blank, blank)

To play 5s and 3s, you put all the dominoes face down, shuffle them about on the table, and each player takes 7 and looks at them but keeps them hidden from the others.  In this person's rules the person with double six starts by placing it down.  Not sure what happens if no one has it; my wife's rules are slightly different at this point.  edit: With 4 players all the dominoes are used up at the start.

The next player must follow with a domino that 'joins' up; eg. (6,1) with the 6 touching the existing sixes.

The next player has to add to either end so can play if they have a domino with another 6 or with a 1.

eg.  (6,6) - (6,1) - (1,4) .......

or

eg.  (5,6) - (6,6) - (1,2) where someone has joined at the other end.

In 5s and 3s you get points if the end total is a multiple of 5 or 3 or both.

eg.  (6,6) - (6,3) scores 8 points because 6 + 6 + 3 = 15 and 15/5 = 3 points plus 15/3 = 5 points.

Note to  nalareddep

(6,6) is a poor opening move.

Better to start with (4,5) because you score three and the best possible score next is two.  I got this from my wife who is a wizard at 5s and 3s.

Bob

Last edited by Bob (2011-09-10 04:25:05)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Double 6 Start

eg.  (5,6) - (6,6) - (1,2) where someone has joined at the other end.

first of all i know what a domino is.

next,i don't think that the statement in the quote above is legit. (6,6)-(1,2)?

last,i never heard of 3's and 5's,but if i am getting the rules correctly (6,6) would give you 4 points?

Last edited by anonimnystefy (2011-09-10 04:29:03)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Double 6 Start

hi Stefy

Yes, (6,6) is 4 points.

next,i don't think that the statement in the quote above is legit. (6,6)-(1,2)?

Whoops.  You're right!  I meant to put (6,1).  Shows my explanation was good though, if you are correcting me. 

In standard dominoes you play to get rid of all yours first.

With 5s and 3s you still do this but you also get points along the way.  The non doubles are placed end to end, but the doubles are placed sideways and both numbers count towards the end total.  Hence the 6 + 6 + 3.

If the chain is

(3,4) - (4,5) - (5,6) - (6,6) - (6,1) - (1, 2)

then the player gets 1 point for 3 + 2 = 5  where 5/5 = 1.

With less than 4 players, you only start with 7 and some are left face down.  If a player cannot go they 'knock' ( tap the table) and take an extra domino.  So it is also skillful to aim always to be able to go if you can.

When I was young, and my wife was as yet just my girlfriend, her family played this a lot.  They were all really good so I got beaten every time.

Bob

Last edited by Bob (2011-09-10 04:42:52)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nalareddep

Member

Registered: 2011-09-10

Posts: 2

Re: Double 6 Start

Hi Bob

Is 66 a bad down if you are not holding the 03 or the 33 ?  Or if you are holding the 63,30 !  But strategy is not the issue I want to analyse the 66 down.

What I want to show is that should you go down with 66 and not hold these dominos 03,33 thereby giving your partner the oppotunity to hold them 2:1 how do the scores of all possibilities add up.  i.e. are scores fairly even.  This would prove that 66 down is not such a dumb move in certain circumstances.

The rules I play to are downs taken in turn
Any domino can start
4 players as partners

I started as per your diagram but it must run into hundreds if not thousands of possible first round of play

If you want to play I helped this guy with strategy for his software

http://www.sadmansoftware.com/fivesandthrees/

Last edited by nalareddep (2011-09-10 09:43:30)