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Old 2007-09-18, 20:57   #1
davar55
 
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May 2004
New York City

3·17·83 Posts
Default A Kind of Solitaire

I recently came across this and thought it might be interesting here:

Start with a deck of T cards where T=n*(n+1)/2 is triangular.

Form a collection of piles of arbitrary sizes using up all T cards.

At each step, take one card away from every pile and with these
removed cards form a new pile.

Then:

(a) Eventually, the piles will have sizes {1,2,3,...,n} after which
each step cycles on this pattern.

(b) This pattern occurs within n*(n-1) steps.

(This is called Bulgarian solitaire and was introduced by Martin Gardner.)

Proofs of (a) and (b) exist, but you're welcome to try.
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