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From: Kevin Stone on 21 Jun 2010 19:35
> Any known unknowns?

Or unknown knowns.

--
Kev


From: Tim Little on 21 Jun 2010 20:20
On 2010-06-21, Leroy Quet <qqquet(a)mindspring.com> wrote:
> A point is scored for a player for every integer in the player's color
> where _______.

.... there are infinitely many pairs of primes separated by twice that
integer.

This could easily be applied by a player who thinks that they will
otherwise lose and would rather the game end in confusion than a
certain loss.


> Any unforeseen problems with this game?

Almost certainly, but I've foreseen this one.


- Tim
From: James Dow Allen on 22 Jun 2010 01:50
On Jun 22, 6:35 am, "Kevin Stone" <newsacco...(a)hotpop.com> wrote:
> > Any known unknowns?
>
> Or unknown knowns.

Didn't you overlook a case? Don Rumsfeld, February 12, 2002:
> There are known knowns. These are things we know that we know.
> There are known unknowns. That is to say, there are things
> that we now know we don’t know. But there are also unknown unknowns.
> These are things we do not know we don’t know."

(Give Rumsfeld credit for his wisdom! If the cabal had heeded
it, they would never have embarked on the Trillion Dollar
Adventure.)

James
From: Leroy Quet on 22 Jun 2010 07:43
Silly people. By unforeseen problems, I meant unforeseen TO ME. :)

(For example, there was an unforeseen problem with my use of the
phrase "unforeseen problems" in the original post.)

Thanks,
Leroy Quet

From: Leroy Quet on 23 Jun 2010 14:42


Leroy Quet wrote:
> This is a simple game that has the potential to go horribly wrong...
>
> This game is for any plural number of players. Let the number of
> players be m.
>
> Each player has a different colored pen/pencil/crayon.
>
> Make a number line with the positions immediately beneath it labeled
> in order with 1 through m*n, where n is some positive integer decided
> ahead of time by the players.
>
> The players take turns. On a PLAYER'S k_th move, he/she writes (with
> the pen/pencil/crayon of his own color) the number k just above any
> one of the empty positions along the number line.
> After every player has written n -- after a total of m*n moves, and
> the number line is filled up -- the next part of the game begins.
> (When the first part of the game is complete, every integer k occurs
> exactly m times on the top of the number line.)
>
> Next, each player comes up with a rule for scoring points.
>
> Each rule completes this sentence:
>
> A point is scored for a player for every integer in the player's color
> where _______.
>
> The rule must be based on the position number (below the line) of the
> integer (above the line) being tested , and/or on the neighboring
> integers written during play (above the line).
>
> A rule must NOT be based on the colors of the integers or on any
> external variables.
>
> The rules may use any mathematics the players personally choose.
>
> All the rules apply to all the players' numbers fairly.
>
> An example of some rules:
>
> A point is scored for a player for every integer k in the player's
> color where _______.
> * k is next to exactly one integer of opposite parity.
> * k = the number of divisors of its position-number.
> * k divides the sum of its immediate neighbors.
> * k is coprime to the sum of all numbers to its left.
>
> (My examples use basic number theory, but you can involve other
> branches of mathematics.)
>
> Largest score wins.
>
> Variation:
> Play on a grid instead of number line.
> Involve the number of the column and/or the number of the row of each
> number being tested, as well as neighboring numbers, possibly.
>
> Any unforeseen problems with this game?
>

I should have been more clear about the fact that the players EACH
come up with a rule, and all the rules are used to test all the
players' numbers, and the points obtained (in respect to all the
rules) by each player are summed.

(So, if one player picks a rule that gives a point for every number,
no matter what the number or color, hopefully someone else's rule will
help determine a winner/loser.)

Thanks,
Leroy Quet

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