| First, consider a more general case. I will use 0, 1, 2, 3 as an
example, but this works for any number of objects. Suppose you have
two stacks, one sorted in repeated ascending order and one sorted in
repeated descending order:
0 3
1 2
2 1
3 0
0 3
1 2
2 1
. .
. .
. .
Now turn the left stack 90 degrees to the right and the right stack 90
degrees to the left and put them next to each other:
...2103210 3210321...
In the center, you have "32103210". Obviously, if you take exactly
four cards from any one location in this sequence, you will get 0, 1,
2, and 3 in some order, and when you close the gap left by the removal,
you will still have a sequence that goes "32103210".
When you riffle shuffle the left stack with the right stack, this is
what you are doing. The riffle shuffle takes some cards from the left
stack and some from the right stack. Each time the shuffle has taken a
total of four cards, no matter how many of those four come from the
left stack and how many from the right stack, the shuffle has taken
four cards from that sequence. Then it takes four more, and four more,
until the stacks are exhausted.
If you had a stack of cards arranged as BRBRBR... and another arranged
as RBRBRB..., you could do the same thing. However, since the
BRBRBR... sequence has only two elements, it can be made into the
RBRBRB... sequence by cutting.
Thus, you can shuffle two stacks that are both BRBRBR... into each
other. When you cut at a point where two cards are the same color, you
are cutting between an R and a B in one sequence and between a B and an
R in the other sequence. The resulting deck is the same as if you had
shuffle at BRBRBR... stack into an RBRBRB... stack.
-- edp
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> Sort a pack of 52 playing cards into red black order.
> Riffle Shuffle the pack.
> Cut at a point where two cards are the same colour (ie. such that the
> top and bottom cards are now the same colour).
> The order of the pack will now be such that each pair of card from the
> top down will contain ane red and one black card (eg. BRRBRBBRRBRB
> etc).
I don't get what you mean by "such that the top and bottom cards are the same
color". If you're talking about the top and bottom cards of the deck before
cutting, what it they're not the same color ? Do we not cut ? Do we shuffle
again and hope ?
If you're talking about the top and bottom cards of each of the two halves of
the deck during the cut, which half ?
Can you reword the whole thing perhaps ?
Thanks.
/Eric
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