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This is a little more than a new game it potentially uncovers a new class of numbers -- though determining membership might become a hard problem.

A number that possesses the solitaire property can be written in as ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc,(where the "0" is the first zero in the number), with a radix point anywhere. We are free to pick the base and say it is solitaire with respect to that base. After the initial 0, the subsequent ordinals (the 1,2, etc or the 1,10,11, etc) used to write the solitaire number don't have to be the first ones. For example:

pi=3.1415926535897932384626433832795
0 2884
1 971693993751058
2 0974944592
3 078163860
4 ...
etc.,

or

pi=3.1415926535897932384626433832795

0 2884197

1 6939937510582 097494459

2 3 07816

3 860
4 ...
etc.,are both acceptable. (If the number can be written as  ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc. it is solitaire.)

The Champernowne constant with respect to base 10 has only one representation:

0.

1

2

3

4

5

6

7

8

9

10

11...

etc. .

 

I know Base 10 Champernowne constant is base 10 solitaire. I can not say the same with certainty for Pi.

I also propose we can measure the solitude of a number by the average amount of numbers between the 0,1,2,3..., and give a perfect solitude score to Base 10 Champernowne constant. Other constants can be given additional credit, of some kind, if the amounts of numbers between the 1,2,3... follow a specific preset pattern.

 

 

marvinrayburns.com

 

my_sol.mw

Leonhard is playing a casino game. He places his bet and then rolls a
pair of dice: if the dice sum to 7, 8 or 9 then Leonhard wins the amount of his
bet, and otherwise Leonhard loses his money. Leonhard begins with $100 and
decides to bet $50 at time, until he has either won $100 or has gone broke. What
are the chances that Leonhard leaves the casino a winner?

My soln doesn't agree with the stated answer..25/74

Maple SOKOBAN game...

August 08 2013 stefbuet 56 Maple

I made 3 years ago a SOKOBAN game using Maple for my Math/Programming class.

Here is a video of the application:

http://www.youtube.com/watch?v=l00l82_LK2Y

Have a nice day!

Does any one know how to derive this model in Maple?

The_Price_is_Righ.pdf

Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team.  Posts in the series include:

  • Part 1 - ...

Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team.  Posts in the series include:

  • Part 1 - 

Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team.  Posts in the series include:

  • Part 1 - 

Poker Probabilities...

January 11 2012 marc005 3048 Maple 13

I have below outlined the different probabilities for different poker hands given
5 cards from a 52 cards deck. The frequencies are from wikipedia
http://en.wikipedia.org/wiki/Poker_probability




These frequencies are quite interesting....I wonder if they found them by "brute fource"

One thing I have always found interesting is that exponential growth/decay
is not symmetrical hence:

100*(1+0.01)^2+100*(1-0.01)^2-200 = 0.0200

For example:

If you start with 100 and bet 1% and you win and then again bet 1% of your portfolio value
and you win again your portfolio value will be PW=100*(1+0.01)^2.

If you start with 100 and bet 1% and you lose and then again bet 1% of your portfolio value
and you lose again your portfolio value will be PL=100*(1-0.01)^2. ...

Sorry that this may not belong here but I thought I would ask, it is interesting. 

Now I'm not asking for the winning numbers list but rather the numbers chosen by people (the thousands of non winning ticket numbers per game)  Is there a database somewhere we can access that stores the list of picked numbers?  It would be interesting to find out how randomly people pick numbers, do people flock to certain numbers more often than others?

I...

Classic Triangle Peg Board GameIn high school I was briefly fascinated by a triangular "jump all but one" game, commonly found at Cracker Barrel restaurants.  The basic premise is that any peg can "jump" over an adjacent peg to occupy the empty hole next to the jumped peg.  The jumped peg is then removed.  The goal is to continue jumping pegs until there is only one left.  


The instructions on the face of the Cracker Barrel version of this game say, "LEAVE ONLY ONE -- YOU'RE A GENIUS".  Wanting to claim the right to call myself a genius, unlike ordinary kids, who might just play the game a few times, I sat down on my Turbo-XT and started writing BASIC code.  The algorithm I came up with ran a bit slow, so I directed output to my printer and let it run over night.  In the morning the program was still chugging along.  I advanced the paper feed on the dot-matrix lineprinter -- the kind that used continuous feed paper with perforated edges and holes on each side.   Into view came 3 solutions represented by a string of numbers.   A quick check verified that I was now a genius.  

Good morning,

I want to  to show the 2-simplex (in R^2) obtained from the inequality

 

x+ y+ z < = 12*a

 with a:=1;

x, y, z  >= 0.

(the angles of the triangle are (12,0,0), (0,12,0) and (0,0,12) )

 

The CORE of a cooperative game, is the set points that additionally satisfy the system

 

x+ y >= 6

x+ z >= 6

y + z >= 6

Just for fun last night I thought I'd try to whip up a simulation of the simple card game war.  The hoyle rulebook - evenly divide the cards up between 2 players facedown, turn over top card, highest card wins.  In the event of a tie the higher of the next overturned card wins (the more common variant is to play 3 facedown cards and turn up the 4th) - but that introduces more complexity to the programming ... I thought I'd tackle that later, but first ...

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