20070918, 20:57  #1 
May 2004
New York City
3×17×83 Posts 
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*(n1) steps. (This is called Bulgarian solitaire and was introduced by Martin Gardner.) Proofs of (a) and (b) exist, but you're welcome to try. 
20070919, 10:51  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}·1,543 Posts 
It is a dull type of solitaire game. Since we know the outcome in advance and there is no strategy at all.
What actually is your puzzle here? 
20070919, 11:44  #3 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 

20070919, 13:21  #4 
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
I have to agree with this sentiment. It seems to me that there have been posted here a number of "mathematical exercises" and/or "conjectures" that we are being ask to solve in the name of a "puzzle".
These contrast highly from those examples such as the "hole in the sphere" or the logic problems that are characteristic of the problems posed by the "Mathematical Recreations" Greats of the last centuries. 
20070919, 14:09  #5  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
I can see why 1,2,3,,,,,n stays as it is. If Martin Gardner posed it, it qualifies for this thread IMHO. What do you think of Nim? David 

20070919, 15:42  #6  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:
In particular, I recall that he popularized John Conway's cellular automaton "Game of Life", as well as many other interesting topics. As for Nim, I worked out the winning strategy decades ago. As a result, I find it of little more interest than Tic Tac Toe. Last fiddled with by Wacky on 20070919 at 15:44 

20070919, 15:49  #7 
"Lucan"
Dec 2006
England
6474_{10} Posts 

20070921, 11:24  #8 
"Lucan"
Dec 2006
England
194A_{16} Posts 
Nim
Well I deem my "Nim" thread a success!
Is a proof of this solitaire puzzle beyond me? It makes a nice little simulation program. David BTW in the light of Mally's demise, I regret my reference to a Bronze medal. Last fiddled with by davieddy on 20070921 at 11:38 
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