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From: Leroy Quet on 21 Jun 2010 16:12
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?

Thanks,
Leroy Quet

From: Richard Heathfield on 21 Jun 2010 17:53
Leroy Quet wrote:

<snip>

> Any unforeseen problems with this game?

Yes. By definition, however, we can't tell you what they are. Otherwise,
they'd be foreseen problems.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
"Usenet is a strange place" - dmr 29 July 1999
Sig line vacant - apply within
From: Kevin Stone on 21 Jun 2010 18:04
>> Any unforeseen problems with this game?

> Yes. By definition

Not necessarily...

What if there were no problems at all, foreseen or unforeseen?

--
Kev


From: Richard Heathfield on 21 Jun 2010 18:19
Kevin Stone wrote:
>>> Any unforeseen problems with this game?
>
>> Yes. By definition
>
> Not necessarily...
>
> What if there were no problems at all, foreseen or unforeseen?

Oh - I hadn't foreseen that possibility. It's a real problem.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
"Usenet is a strange place" - dmr 29 July 1999
Sig line vacant - apply within
From: Calvin on 21 Jun 2010 19:29
On Tue, 22 Jun 2010 08:19:40 +1000, Richard Heathfield
<rjh(a)see.sig.invalid> wrote:

> Kevin Stone wrote:
>>>> Any unforeseen problems with this game?
>>
>>> Yes. By definition
>> Not necessarily...
>> What if there were no problems at all, foreseen or unforeseen?
>
> Oh - I hadn't foreseen that possibility. It's a real problem.

Any known unknowns?

--

cheers,
calvin
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