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--- no_problem [2023/03/24 21:01]
harshec created
+++ no_problem [2023/03/25 19:01] (current)
harshec
@@ Line 1: / Line 1: @@
 ====A Solution Looking For A Problem====
-In an attempt to deflect emails and other correspondence from people who are wondering what the point of all of this is, let me state upfront: I understand that there are //plenty// of ways to quickly determine who goes first in a game.
+In an attempt to deflect emails and other correspondence from people who are wondering what the point of all of this is, let me (Eric) state upfront: I understand that there are //plenty// of ways to quickly determine who goes first in a game.
-This mathematics of this research problem quickly overshadowed its practicality. If you want to determine who goes first in a game, just roll dice... standard dice. Sure you may have to reroll ties, but I'm sure you'll manage. Or, get all of the spades from a deck of cards and have each player draw one randomly... that'll suffice for up to 13 players.
+The mathematics of this research problem long ago overshadowed its practicality. If you want to determine who goes first in a game, just roll dice... standard dice. Sure you may have to reroll ties, but I'm sure you'll manage. Or, get all of the spades from a deck of cards and have each player draw one randomly... that'll suffice for up to 13 players.
+{{  http://www.ericharshbarger.org/dice/gfd_02.jpg?300}}
 For that matter, if you want to create custom dice, you can fairly pick a random permutation for up to five players with a //single// die. The number of orderings of //n// players is //n//!:
   * 2! == 2
@@ Line 10: / Line 11: @@
   * 5! == 120
-So, for a three players, an specially designed d6 with "abc", "acb", "bac", bca", cab", and "cba" on the faces will, with a single roll, tell you what order the three players should play in (hey! I actually //do// make such custom dice, and you [[https://mathartfun.com/dSpecial.html|find them for sale here at MathArtFun]]).
+So, for a three players, a specially designed d6 with "abc", "acb", "bac", bca", cab", and "cba" on the faces will, with a single roll, tell you what order the three players should play in (hey! I actually //do// make such custom dice, and [[https://mathartfun.com/dSpecial.html|you can find them for sale here at MathArtFun]]).
-There exist pleasant shapes for 24-sided dice, so the 4 player orderings could be determined with a single roll (sorry, I don't make custom d24s). Even 5 players can be accommodated with a single roll of a specially made d120. In fact, I 3D printed such a d120 (pictured here), but gave up inking it (it's also a bit too massive to be conveniently rolled). {{http://www.ericharshbarger.org/dice/gfd_02.jpg}}
+There exist pleasant shapes for 24-sided dice, so the 4 player orderings could be determined with a single roll (sorry, I don't make custom d24s). Even 5 players can be accommodated with a single roll of a specially made d120. In fact, I 3D printed such a d120 (pictured at right), but gave up inking it (it's also a bit too massive to be conveniently rolled).
+So, sure, the research being done on the Go first Dice problem is not solving a huge problem. But, //mathematically// speacking, it's a pretty interesting topic (at least to me, and a few others). And besides, there is something cool about using a set of Go First Dice, each player getting to roll his or her own die, and //knowing// there will be no ties, and the numberings are perfectly fair...

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