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.
Col. George Sicherman
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