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The Magic Cafe Forum Index » » Magical equations » » Domino Principle - using six colors (0 Likes) Printer Friendly Version

Mindbender
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A while back there was a discussion on using the Domino Principle. See:

http://www.themagiccafe.com/forums/viewt......forum=99

In that discussion, Dan Harlan explained how to make an endless chain with five colors. I quote:
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Using five colors (Red, Orange, Yellow, Green, Blue) there are exactly 10 ways to pair them mis-matched:
R/O R/Y R/G R/B
O/Y O/G O/B
Y/G Y/B
G/B

You'll notice that it's easy to create this set by starting with the first color (R) and pairing it in succession with each color that follows it. Then move onto the second color (O) and pair it only with the colors that follow it (since it has already been paired with Red). Continue with each color.
___________________________________________________________________________

Now for my dilemma:

I want to use 6 colors instead of 5, and put them on poker chips. That would mean 15 poker chips in all.

The colors I am using are: Green, Yellow, White, Red, Orange

The combinations are:

G/Y G/B G/W G/R G/O
Y/B Y/W Y/R Y/O
B/W B/R B/O
W/R W/O
R/O

Unfortunately, this doesn't seem to work. The poker chips "dead end" before all the chips are used. Any idea what I am doing wrong? If you would like to play around with my combinations, you could write the colors on scraps of paper and try it out.

Thanks,
Richard
Philemon Vanderbeck
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No, it won't... no matter what you try to do.

The problem is you have a total of 5 pairs that each contain the color green. You can match four of them in two pairs, but that leaves one green as odd man out. (Of course, this holds true with any color.)

If you're still committed to a six-color theme, then you'll have to put in "double pairs" of the same color, and even then you might have problems.

The other solution is to bump it up to seven colors, which will again work.

Or you could remove selected pairs eliminating the odd colors (like the R/W, Y/B and O/G).
Professor Philemon Vanderbeck
That Creepy Magician
"I use my sixth sense to create the illusion of possessing the other five."
Mindbender
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Thank, Philemon. It works perfectly when I add a seventh color.

On a sidenote, I found that "eliminating the odd colors (like the R/W, Y/B and O/G)" doesn't fix the problem. I did a number of trials with the three suggested chips removed. About 50% of the trials were successful, but the 50% dead-ended before all the chips were used.

Thanks again,
Richard
Philemon Vanderbeck
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Make sure that if you dead end in one direction, to try again from the other end (where you started).
Professor Philemon Vanderbeck
That Creepy Magician
"I use my sixth sense to create the illusion of possessing the other five."
Mindbender
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I have been flipping the stack over when necessary, but to no avail on 1/2 of my test trials.

Let's say I start with the following (the set-up from my original posting), so that I am working with:

G/Y G/B G/W G/R G/O
Y/B Y/W Y/R Y/O
B/W B/R B/O
W/R W/O
R/O

If I remove R/W, Y/B and O/G as suggested, that leaves me with:

G/Y G/B G/W G/R
Y/W Y/R Y/O
B/W B/R B/O
W/O
R/O

Here is one instance where I "dead-end" after seven chips:

R/O - O/W - W/B - B/R - R/G - G/Y - Y/R

At this point there are no more red-sided chips. So as far as I can see, it is not possible to use the domino principle using six colors.

Thoughts anyone?
Philemon Vanderbeck
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It's a little contrived, but you could always have the spectator "cut" the stack, and as long as you don't hit red again, you can have them continue...
Professor Philemon Vanderbeck
That Creepy Magician
"I use my sixth sense to create the illusion of possessing the other five."
Mindbender
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Now that I have the formula worked out, I was wondering if anyone had any ideas on how to color the chips. A friend of mine tried spray painting some plastic poker chips, but the paint didn't adhere very well.

My interim solution (so I can start using the routine) has been to glue large colored stickers (from the stationary store) to the centers of a stack of disks. Alas, this gives them a homemade look.

Any suggestions on how to color poker chips - either just the centers - or the entire faces - that would give them a factory-made appearance?
Philemon Vanderbeck
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You may want to try enamel paint that's used for plastic model kits.
Professor Philemon Vanderbeck
That Creepy Magician
"I use my sixth sense to create the illusion of possessing the other five."
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