Sylver Coinage
Definition
Sylver Coinage is a mathematical
game invented by John Horton Conway.
Two players take turns choosing numbers, which represent denominations
of money.
A player may not name a number that can be expressed as a sum
(with multiples) of some previously chosen numbers.
The player who names 1 loses.
News of Sylver Coinage
Statement of the Progression Hypothesis
Care and Feeding of Enders
A Glossary of Sylver Coinage
Richard K. Guy's Twenty Questions
Tables
 Some Very Long Positions
 Winning Moves in {m,n} Positions
 Some 𝓟Positions With g>1
 Responses to Moves in {14,26}
 Responses to Moves
in {16,22,24,26,28,30,34}
 Responses to Moves in {18,30,32}
 Winning Odd Moves in Even 6Positions
 Winning Moves in Positions with
Numbers 6–14
Refereed Papers
Reports
 New Results In Sylver Coinage (1991)
[ GNUzipped DVI 
PostScript ]
Summary of previous work, many new computational results,
proof of the Single Win Theorem, and a short bibliography.

Late News of Sylver Coinage (1996)
[ GNUzipped DVI
 PostScript
]
Some advanced computational results, including the solution of
{8,30,34} and a new long even position with no odd winning move.

Sylver Coinage positions with g=2 (2021), by Thomas Blok.
Full analysis of all even positions containing an even number from 2 to 10.
[ Microsoft Word
 Adobe Portable
Document Format (PDF)
]

Sylver Coinage even positions in 14 (2022), by Thomas Blok.
Full analysis of all even positions containing the number 14.
[ Adobe Portable
Document Format (PDF)
]
Software
My production software is not yet available.
Meanwhile, here is a simple Perl script
for computing winning moves in Sylver Coinage positions.
Online Service
Sigurd Kittilsen told me about
this
online Sylver Coinage tool.
It was programmed by Roger Antonsen.
Col. George Sicherman
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