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 2007-09-18, 20:57 #1 davar55     May 2004 New York City 5×7×112 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*(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.
 2007-09-19, 10:51 #2 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 33·239 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?
2007-09-19, 11:44   #3
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by retina What actually is your puzzle here?
To prove a) and b)

2007-09-19, 13:21   #4
Wacky

Jun 2003
The Texas Hill Country

32·112 Posts

Quote:
 Originally Posted by retina What actually is your puzzle here?
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.

2007-09-19, 14:09   #5
davieddy

"Lucan"
Dec 2006
England

647410 Posts

Quote:
 Originally Posted by Wacky 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.
Well I am working on it with enthusiasm ATM.
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

2007-09-19, 15:42   #6
Wacky

Jun 2003
The Texas Hill Country

32×112 Posts

Quote:
 Originally Posted by davieddy If Martin Gardner posed it, it qualifies for this thread IMHO. What do you think of Nim?
I will note that Martin Gardner presented many mathematically related topics which were not "puzzles" in the sense of Henry Dudeney or Sam Loyd.

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 2007-09-19 at 15:44

2007-09-19, 15:49   #7
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by Wacky 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.
Do you want a "Bronze medal"

 2007-09-21, 11:24 #8 davieddy     "Lucan" Dec 2006 England 2×3×13×83 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 2007-09-21 at 11:38

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